NCERT Solutions for Class 9 Maths chapter 13 Exercise 13.4 – Surface Areas and Volumes
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Here we have listed Class 9 maths chapter 13 exercise 13.4 solutions in PDF that is prepared by Kota’s top IITian’s Faculties by keeping Simplicity in mind.

If you want to score high in your class 9 Maths Exam then it is very important for you to have a good knowledge of all the important topics, so to learn and practice those topics you can use eSaral NCERT Solutions.

In this article, we have listed NCERT Solutions for Class 9 Maths chapter 13 Exercise 13.4 that you can download to start your preparations anytime.

So, without wasting more time Let’s start.

Download The PDF of NCERT Solutions for Class 9 Maths chapter 13 Exercise 13.4 “Surface Areas and Volumes”

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All Questions of Chapter 13 Exercise 13.4

Once you complete the chapter 13 then you can revise Ex. 13.4 by solving following questions

Q1. Find the surface area of a sphere of radius:
(i) $10.5 \mathrm{~cm}$
(ii) $5.6 \mathrm{~cm}$
(iii) $14 \mathrm{~cm}$

Q2. (i) Find the surface area of a sphere of diameter 14cm.

Q3. Find the total surface area of a hemisphere of radius $10 \mathrm{~cm}$. (Use $\pi=3.14$)

Q4. The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.

Q5. A hemispherical bowl made of brass has inner diameter $10.5 \mathrm{~cm}$. Find the cost of tin-plating it on the inside at the rate of $\mathrm{Rs} 16$ per $100 \mathrm{~cm}^{2}$.

Q6. Find the radius of a sphere whose surface area is $154 \mathrm{~cm} ^ {2}$

Q7. The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

Q8. A hemispherical bowl is made of steel, $0.25 \mathrm{~cm}$ thick. The inner radius of the bowl is $5 \mathrm{~cm}$. find the outer curved surface area of the bowl.

Q9. A right circular cylinder just encloses a sphere of radius $\mathrm{r}$. Find
(i) Surface area of the sphere,
(ii) Curved surface area of the cylinder,
(iii) Ratio of the areas obtained in (i) and (ii).

NCERT Class 9 Maths Book Free PDF

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Complete Solutions for Class 9 Maths chapter 13 Free PDF

Class 9 Maths Chapter 12 Exercise 12.1 Free Solutions PDF

Class 9 Maths Chapter 12 Exercise 12.2 Free Solutions PDF

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NCERT Solutions for Class 9 Maths chapter 13 Exercise 13.3 – Surface Areas and Volumes
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Here we have listed Class 9 maths chapter 13 exercise 13.3 solutions in PDF that is prepared by Kota’s top IITian’s Faculties by keeping Simplicity in mind.

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In this article, we have listed NCERT Solutions for Class 9 Maths chapter 13 Exercise 13.3 that you can download to start your preparations anytime.

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NCERT Class 9 Maths Book PDF

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Complete Solutions for Class 9 Maths chapter 13 PDF

Class 9 Maths Chapter 12 Exercise 12.1 Solutions PDF

Class 9 Maths Chapter 12 Exercise 12.2 Solutions PDF

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NCERT Solutions for Class 9 Maths chapter 13 Exercise 13.2 – Surface Areas and Volumes
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Here we have listed Class 9 maths chapter 13 exercise 13.2 solutions in PDF that is prepared by Kota’s top IITian’s Faculties by keeping Simplicity in mind.

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In this article, we have listed NCERT Solutions for Class 9 Maths chapter 13 Exercise 13.2 that you can download to start your preparations anytime.

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All Questions of Chapter 13 Exercise 13.2

Once you complete the chapter 13 then you can revise Ex. 13.2 by solving following questions

Q1. The curved surface area of a right circular cylinder of height $14 \mathrm{~cm}$ is $88 \mathrm{~cm}^{2}$. Find the diameter of the base of the cylinder.

Q2. It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square metres of the sheet are required for the same?

Q3. A metal pipe is $77 \mathrm{~cm}$ long. The inner diameter of a cross section is $4 \mathrm{~cm}$, the outer diameter being $4.4 \mathrm{~cm}$. Find its :
(i) inner curved surface area,
(ii) outer curved surface area,
(iii) total surface area.

Q4. The diameter of a roller is $84 \mathrm{~cm}$ and its length is $120 \mathrm{~cm}$. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in $\mathrm{m}^{2}$.

Q5. A cylindrical pillar is $50 \mathrm{~cm}$ in diameter and $3.5 \mathrm{~m}$ in height. Find the cost of painting the curved surface of the pillar at the rate of Rs $12.50$ per $\mathrm{m}^{2}$.

Q6. Curved surface area of a right circular cylinder is $4.4 \mathrm{~m}^{2}$. If the radius of the base of the cylinder is $0.7 \mathrm{~m}$, find its height.

Q7. The inner diameter of a circular well is $3.5 \mathrm{~m}$. It is $10 \mathrm{~m}$ deep. Find
(i) its inner curved surface area,

Q8. In a hot water heating system, there is a cylindrical pipe of length $28 \mathrm{~m}$, and diameter $5 \mathrm{~cm}$. Find the total radiating surface in the system.

Q9. Find
(i) The lateral or curved surface area of a closed cylindrical petrol storage tank that is $4.2 \mathrm{~m}$ in diameter and $4.5 \mathrm{~m}$ high.
(ii) How much steel was actually used, if $1 / 12$ of the steel actually used was wasted in making the tank.

Q10. In figure, you see the frame of a lampshade. It is to be covered with a decorative cloth. The frame has a base diameter of $20 \mathrm{~cm}$ and height of $30 \mathrm{~cm}$. A margin of $2.5 \mathrm{~cm}$ is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade.

Q11. The students of a Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius $3 \mathrm{~cm}$ and height $10.5 \mathrm{~cm}$. The Vidyalaya was to supply the competitiors with carboard. If there were 35 competitors, how much cardboard was required to be brought for the competition?

NCERT Class 9 Maths Book

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Complete Solutions for Class 9 Maths chapter 13

Class 9 Maths Chapter 12 Exercise 12.1 Solutions

Class 9 Maths Chapter 12 Exercise 12.2 Solutions

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NCERT Solutions for Class 9 Maths chapter 13 Exercise 13.1 – Surface Areas and Volumes
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Here we have listed Class 9 maths chapter 13 exercise 13.1 solutions in PDF that is prepared by Kota’s top IITian’s Faculties by keeping Simplicity in mind.

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In this article, we have listed NCERT Solutions for Class 9 Maths chapter 13 Exercise 13.1 that you can download to start your preparations anytime.

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All Questions of Chapter 13 Exercise 13.1

Once you complete the chapter 13 then you can revise Ex. 13.1 by solving following questions

Q1. A plastic box $1.5 \mathrm{~m}$ long, $1.25 \mathrm{~m}$ wide and $65 \mathrm{~cm}$ deep is to be made. It is opened at the top. Ignoring the thickness of the plastic sheet, determine:
(i) The area of the sheet required for making the box.
(ii) The cost of sheet for it, if a sheet measuring $1 \mathrm{~m}^{2}$ costs Rs 20.

Q2. The length, breadth and height of a room are $5 \mathrm{~m}, 4 \mathrm{~m}$ and $3 \mathrm{~m}$ respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs $7.50$ per $\mathrm{m}^{2}$.

Q3. The floor of a rectangular hall has a perimeter $250 \mathrm{~m}$. If the cost of painting the four walls at the rate of Rs. 10 per $\mathrm{m}^{2}$ is Rs. 15000, find the height of the hall.

Q4. The paint in a certain container is sufficient to paint an area equal to $9.375 \mathrm{~m}^{2}$. How many bricks of dimensions $22.5 \mathrm{~cm} \times 10 \mathrm{~cm} \times 7.5 \mathrm{~cm}$ can be painted out of this container?

Q5. A cubical box has each edge $10 \mathrm{~cm}$ and another cuboidal box is $12.5 \mathrm{~cm}$ long, $10 \mathrm{~cm}$ wide and $8 \mathrm{~cm}$ high.
(i) Which box has the greater lateral surface area and by how much?
(ii) Which box has the smaller total surface area and by how much?

Q6. A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is $30 \mathrm{~cm}$ long, $25 \mathrm{~cm}$ wide and $25 \mathrm{~cm}$ high.
(i) What is the area of the glass?
(ii) How much of tape is needed for all the 12 edges?

Q7. Shanti Sweets Stall was placing an order for making carboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions $25 \mathrm{~cm} \times 20 \mathrm{~cm} \times 5 \mathrm{~cm}$ and the smaller of dimensions $15 \mathrm{~cm} \times 12 \mathrm{~cm} \times 5 \mathrm{~cm}$. For all the overlaps, $5 \%$ of the total surface area is required extra. If the cost of the card board is Rs. 4 for $1000 \mathrm{~cm}^{2}$, find the cost of cardboard required for supplying 250 boxes of each kind.

Q8. Parveen wanted to make a temporary shelter for her car, by making a box-like structure with tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height $2.5 \mathrm{~m}$, with base dimensions $4 \mathrm{~m} \times 3 \mathrm{~m} ?$

Download Complete Solutions for Class 9 Maths chapter 13

Download Class 9 Maths Chapter 12 Exercise 12.1 Solutions

Download Class 9 Maths Chapter 12 Exercise 12.2 Solutions

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NCERT Solutions for Class 9 Maths chapter 12 Exercise 12.2 – Heron’s Formula
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Here we have listed Class 9 maths chapter 12 exercise 12.2 solutions in PDF that is prepared by Kota’s top IITian’s Faculties by keeping Simplicity in mind.

If you want to score high in your class 9 Maths Exam then it is very important for you to have a good knowledge of all the important topics, so to learn and practice those topics you can use eSaral NCERT Solutions.

In this article, we have listed NCERT Solutions for Class 9 Maths chapter 12 Exercise 12.2 that you can download to start your preparations anytime.

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Download The PDF of NCERT Solutions for Class 9 Maths chapter 12 Exercise 12.2 “Heron’s Formula”

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All Questions of Chapter 12 Exercise 12.2

Once you complete the chapter 12 then you can revise Ex. 12.2 by solving following questions

Q1. A park, in the shape of a quadrilateral $\mathrm{ABCD}$ has $\angle \mathrm{C}=90^{\circ}, \mathrm{AB}=9 \mathrm{~m}, \mathrm{BC}=12 \mathrm{~m}$, $\mathrm{CD}=5 \mathrm{~m}, \mathrm{AD}=8 \mathrm{~m} .$ How much area does it occupy ?

Q2. Find the area of quadrilateral $\mathrm{ABCD}$ in which $\mathrm{AB}=3 \mathrm{~cm}, \mathrm{BC}=4 \mathrm{~cm}, \mathrm{CD}=4 \mathrm{~cm}$, $\mathrm{DA}=5 \mathrm{~cm}$ and $\mathrm{AC}=5 \mathrm{~cm}$.

Q3. Radha made a picture of an aeroplane with coloured paper as shown in Fig. find the total area of the paper used.

Q4. A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

Q5. A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 cm and its longer diagonal is 48 cm, how much area of grass field will each cow be getting?

Q6. An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see Fig.) each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella ?

Q7. A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in Fig. How much paper of each shade has been used in it ?

Q8. A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being $9 \mathrm{~cm}, 28 \mathrm{~cm}$ and $35 \mathrm{~cm}$ (See Fig.). Find the cost of polishing the tiles at the rate of 50 $\mathrm{p}$ per $\mathrm{cm}^{2}$.

Q9. A field is in the shape of a trapezium whose parallel sides are $25 \mathrm{~m}$ and $10 \mathrm{~m}$. The non-parallel sides are $14 \mathrm{~m}$ and $13 \mathrm{~m}$. Find the area of the field.

NCERT Class 9 Maths Book

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Complete Solutions for Class 9 Maths chapter 12

Class 9 Maths Chapter 11 Exercise 11.1 Solutions

Class 9 Maths Chapter 11 Exercise 11.2 Solutions

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NCERT Solutions for Class 9 Maths chapter 12 Exercise 12.1 – Heron’s Formula
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Here we have listed Class 9 maths chapter 12 exercise 12.1 solutions in PDF that is prepared by Kota’s top IITian’s Faculties by keeping Simplicity in mind.

If you want to score high in your class 9 Maths Exam then it is very important for you to have a good knowledge of all the important topics, so to learn and practice those topics you can use eSaral NCERT Solutions.

In this article, we have listed NCERT Solutions for Class 9 Maths chapter 12 Exercise 12.1 that you can download to start your preparations anytime.

So, without wasting more time Let’s start.

Download The PDF of NCERT Solutions for Class 9 Maths chapter 12 Exercise 12.1 “Heron’s Formula”

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All Questions of Chapter 12 Exercise 12.1

Once you complete the chapter 12 then you can revise Ex. 12.1 by solving following questions

Q1. A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is $180 \mathrm{~cm}$, what will be the area of the signal board ?

Q2. The triangular side walls of a flyover have been used for advertisements. The sides of the walls are $122 \mathrm{~m}, 22 \mathrm{~m}$ and $120 \mathrm{~m}$ (see Fig.). The advertisements yield as earning of Rs. 5000 per $\mathrm{m}^{2}$ per year. A company hired one of its walls for 3 months. How much rent did it pay ?

Q3. There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN” (see Fig.). If the sides of the wall are $15 \mathrm{~m}, 11$ $\mathrm{m}$ and $6 \mathrm{~m}$, find the area painted in colour.

Q4. Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.

Q5. Sides of a triangle are in the ratio of 12: 17: 25 and its perimeter is 540 cm. Find its area.

Q6. An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of triangle.

Download Complete Solutions for Class 9 Maths chapter 12

Download Class 9 Maths Chapter 11 Exercise 11.1 Solutions

Download Class 9 Maths Chapter 11 Exercise 11.2 Solutions

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NCERT Solutions for Class 9 Maths chapter 11 Exercise 11.2 – Constructions
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Here we have listed Class 9 maths chapter 11 exercise 11.2 solutions in PDF that is prepared by Kota’s top IITian’s Faculties by keeping Simplicity in mind.

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In this article, we have listed NCERT Solutions for Class 9 Maths chapter 11 Exercise 11.2 that you can download to start your preparations anytime.

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Download The PDF of NCERT Solutions for Class 9 Maths chapter 11 Exercise 11.2 “Constructions”

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All Questions of Chapter 11 Exercise 11.2

Once you complete the chapter 11 then you can revise Ex. 11.2 by solving following questions

Q1. Construct a triangle ABC in which BC = 7 cm, B = 75° and AB + AC = 13 cm.

Q2. $\quad$ Construct a triangle $\mathrm{ABC}$ in which $\mathrm{BC}=8 \mathrm{~cm}, \angle \mathrm{B}=45^{\circ}$ and $\mathrm{AB}-\mathrm{AC}=3 \cdot 5 \mathrm{~cm}$.

Q3. Construct a triangle $\mathrm{PQR}$ in which $\mathrm{QR}=6 \mathrm{~cm}, \angle \mathrm{Q}=60^{\circ}$ and $\mathrm{PR}-\mathrm{PQ}=2 \mathrm{~cm}$.

Q4. Construct a triangle $\mathrm{XYZ}$ in which $\angle \mathrm{Y}=30^{\circ}, \angle \mathrm{Z}=90^{\circ}$ and $\mathrm{XY}+\mathrm{YZ}+\mathrm{ZX}=11 \mathrm{~cm}$.

Q5. Construct a right triangle whose base is 12 cm and sum of its hypotenuse and other side is 18 cm.

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Download Complete Solutions for Class 9 Maths chapter 11

Download Class 9 Maths Chapter 10 Exercise 10.1 Solutions

Download Class 9 Maths Chapter 10 Exercise 10.2 Solutions

Download Class 9 Maths Chapter 10 Exercise 10.3 Solutions

Download Class 9 Maths Chapter 10 Exercise 10.4 Solutions

Download Class 9 Maths Chapter 10 Exercise 10.5 Solutions

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NCERT Solutions for Class 9 Maths chapter 11 Exercise 11.1 – Constructions
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Here we have listed Class 9 maths chapter 11 exercise 11.1 solutions in PDF that is prepared by Kota’s top IITian’s Faculties by keeping Simplicity in mind.

If you want to score high in your class 9 Maths Exam then it is very important for you to have a good knowledge of all the important topics, so to learn and practice those topics you can use eSaral NCERT Solutions.

In this article, we have listed NCERT Solutions for Class 9 Maths chapter 11 Exercise 11.1 that you can download to start your preparations anytime.

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Download The PDF of NCERT Solutions for Class 9 Maths chapter 11 Exercise 11.1 “Constructions”

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All Questions of Chapter 11 Exercise 11.1

Once you complete the chapter 11 then you can revise Ex. 11.1 by solving following questions

Q1. Construct an angle of $90^{\circ}$ at the initial point of a given ray and justify the construction.

Q2. Construct an angle of 45° at the initial point of a given ray and justify the construction.

Q3. Construct the angles of the following measurements:
(i) $30^{\circ}$
(ii) $22 \frac{1}{2}$ o
(iii) $15^{\circ}$

Q4. Construct the following angles and verify by measuring them by a protractor:
(i) $75^{\circ}$
(ii) $105^{\circ}$
(iii) $135^{\circ}$

Q5. Construct an equilateral triangle, given its side and justify the construction.

Download Complete Solutions for Class 9 Maths chapter 11 PDF

Download Class 9 Maths Chapter 10 Exercise 10.1 Solutions PDF

Download Class 9 Maths Chapter 10 Exercise 10.2 Solutions PDF

Download Class 9 Maths Chapter 10 Exercise 10.3 Solutions PDF

Download Class 9 Maths Chapter 10 Exercise 10.4 Solutions PDF

Download Class 9 Maths Chapter 10 Exercise 10.5 Solutions PDF

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NCERT Solutions for Class 9 Maths chapter 10 Exercise 10.5 – Circles – Free PDF Download
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Here we have listed Class 9 maths chapter 10 exercise 10.5 solutions in PDF that is prepared by Kota’s top IITian’s Faculties by keeping Simplicity in mind.

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In this article, we have listed NCERT Solutions for Class 9 Maths chapter 10 Exercise 10.5 that you can download to start your preparations anytime.

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Download The PDF of NCERT Solutions for Class 9 Maths chapter 10 Exercise 10.5 “Circles”

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All Questions of Chapter 10 Exercise 10.5

Once you complete the chapter 10 then you can revise Ex. 10.5 by solving following questions

Q1. In Fig. A, B and C are three points on a circle with centre $\mathrm{O}$ such that $\angle \mathrm{BOC}=30^{\circ}$ and $\angle \mathrm{AOB}=60^{\circ} .$ If $\mathrm{D}$ is a point on the circle other than the arc $\angle \mathrm{ABC}$, find $\angle \mathrm{ADC}$.

Q2. A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.

Q3. In figure, $\angle \mathrm{PQR}=100^{\circ}$, where $\mathrm{P}, \mathrm{Q}$ and $\mathrm{R}$ are points on a circle with centre $\mathrm{O}$. Find $\angle \mathrm{OPR}$.

Q4. In fig. $\angle \mathrm{ABC}=69^{\circ}, \angle \mathrm{ACB}=31^{\circ}$, find $\angle \mathrm{BDC}$.

Q5. In figure, $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and $\mathrm{D}$ are four points on a circle. AC and BD intersect at a point $\mathrm{E}$ such that $\angle \mathrm{BEC}=130^{\circ}$ and $\angle \mathrm{ECD}=20^{\circ} .$ Find $\angle \mathrm{BAC}$.

Q6. $\quad \mathrm{ABCD}$ is a cyclic quadrilateral whose diagonals intersect at a point $\mathrm{E}$. If $\angle \mathrm{DBC}=70^{\circ}$, $\angle \mathrm{BAC}=$ is $30^{\circ}$, find $\angle \mathrm{BCD}$. Further, if $\mathrm{AB}=\mathrm{BC}$, find $\angle \mathrm{ECD}$.

Q7. If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

Q8. If the non-parallel sides of a trapezium are equal, prove that it is cyclic.

Q9. Two circles intersect at two points $\mathrm{B}$ and $\mathrm{C}$. Through $\mathrm{B}$, two line segment $\mathrm{ABD}$ and $\mathrm{PBQ}$ are drawn to intersect the circles at $\mathrm{A}, \mathrm{D}$ and $\mathrm{P}, \mathrm{Q}$ respectively. Prove that $\angle \mathrm{ACP}=\angle \mathrm{QCD}$.

Q10. If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.

Q11. $\mathrm{ABC}$ and $\mathrm{ADC}$ are two right triangles with common hypotenuse $\mathrm{AC}$. Prove that $\angle \mathrm{CAD}=\angle \mathrm{CBD}$.

Q12. Prove that a cyclic parallelogram is a rectangle.

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Download Complete Solutions for Class 9 Maths chapter 10 PDF

Download Class 9 Maths Chapter 9 Exercise 9.1 Solutions PDF

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Download Class 9 Maths Chapter 9 Exercise 9.3 Solutions PDF

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NCERT Solutions for Class 9 Maths chapter 10 Exercise 10.4 – Circles – Free PDF Download
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In this article, we have listed NCERT Solutions for Class 9 Maths chapter 10 Exercise 10.4 that you can download to start your preparations anytime.

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Download The PDF of NCERT Solutions for Class 9 Maths chapter 10 Exercise 10.4 “Circles”

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All Questions of Chapter 10 Exercise 10.4

Once you complete the chapter 10 then you can revise Ex. 10.4 by solving following questions

Q1. Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of common chord.

Q2. If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.

Q3. If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.

Q4. If a line intersects two concentric circles (circles with the same centre) with centre $\mathrm{O}$ at $\mathrm{A}$, $\mathrm{B}, \mathrm{C}$ and $\mathrm{D}$, prove that $\mathrm{AB}=\mathrm{CD}$ (see fig).

Q5. Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5 m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is 6 m each, what is the distance between Reshma and Mandip?

Q6. A circular park of radius 20 m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of the string of each phone.

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All Questions of Chapter 10 Exercise 10.3

Once you complete the chapter 10 then you can revise Ex. 10.3 by solving following questions

Q1. Draw different pairs of circles. How many points does each pair have in common ? What is the maximum number of common points ?

Q2. Suppose you are given a circle. Give the construction to find its centre.

Q3. If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.

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In this article, we have listed NCERT Solutions for Class 9 Maths chapter 10 Exercise 10.2 that you can download to start your preparations anytime.

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All Questions of Chapter 10 Exercise 10.2

Once you complete the chapter 10 then you can revise Ex. 10.2 by solving following questions

Q1. Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.

Q2. Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

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Class 9 Maths Chapter 9 Exercise 9.3 Solutions

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All Questions of Chapter 10 Exercise 10.1

Once you complete the chapter 10 then you can revise Ex. 10.1 by solving following questions

Q1. Fill in the blanks
(i) The centre of a circle lies in ………….. of the circle. (exterior, interior)
(ii) A point, whose distance from the centre of a circle is greater than its radius lies in…………..of the circle. (exterior/interior)
(iii) The longest chord of a circle is a…………….of the circle.
(iv) An arc is a………..when its ends are the ends of a diameter.
(v) Segment of a circle is the region between an arc and……….of the circle.
(vi) A circle divides the plane, on which it lies, in ……………. parts.

Q2. Write true or false : Give reasons for your answers.
(i) Line segment joining the centre to any point on the circle is a radius of the circle.
(ii) A circle has only finite number of equal chords.
(iii) If a circle is divided into three equal arcs, each is a major arc.
(iv) A chord of a circle, which is twice as long as its radius, is a diameter of the circle.
(v) Sector is the region between the chord and its corresponding arc.
(vi) A circle is a plane figure.

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In this article, we have listed NCERT Solutions for Class 9 Maths chapter 9 Exercise 9.3 that you can download to start your preparations anytime.

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All Questions of Chapter 9 Exercise 9.3

Once you complete the chapter 9 then you can revise Ex. 9.3 by solving following questions

Q1. In fig, E is any point on median AD of a $\Delta \mathrm{ABC}$. Show that ar $(\mathrm{ABE})=\operatorname{ar}(\mathrm{ACE})$.

Q2. In a triangle $\mathrm{ABC}, \mathrm{E}$ is the mid-point of median $\mathrm{AD}$. Show that ar $(\mathrm{BED})=\frac{1}{4} \operatorname{ar}(\mathrm{ABC})$.

Q3. Show that the diagonals of a parallelogram divide it into four triangles of equal area.

Q4. In fig, $\mathrm{ABC}$ and $\mathrm{ABD}$ are two triangles on the same base $\mathrm{AB}$. If line- segment $\mathrm{CD}$ is bisected by $\mathrm{AB}$ at $\mathrm{O}$, show that $\operatorname{ar}(\mathrm{ABC})=\operatorname{ar}(\mathrm{ABD})$.

Q5. D, E and $\mathrm{F}$ are respectively the mid-points of the sides $\mathrm{BC}, \mathrm{CA}$ and $\mathrm{AB}$ of $\mathrm{a} \triangle \mathrm{ABC}$. Show that
(i) $\mathrm{BDEF}$ is a parallelogram.
(ii) $\operatorname{ar}(\mathrm{DEF})=\frac{1}{4} \operatorname{ar}(\mathrm{ABC})$
(iii) ar $(\mathrm{BDEF})=\frac{1}{2}$ ar $(\mathrm{ABC})$

Q6. In fig, diagonals AC and BD of quadrilateral ABCD intersect at $\mathrm{O}$ such that $\mathrm{OB}=\mathrm{OD}$. If $\mathrm{AB}=\mathrm{CD}$, then show that :

(i) $\operatorname{ar}(\mathrm{DOC})=\operatorname{ar}(\mathrm{AOB})$
(ii) $\operatorname{ar}(\mathrm{DCB})=\operatorname{ar}(\mathrm{ACB})$
(iii) $\mathrm{DA} \| \mathrm{CB}$ or $\mathrm{ABCD}$ is a parallelogram.

Q7. $\mathrm{D}$ and $\mathrm{E}$ are points on sides $\mathrm{AB}$ and $\mathrm{AC}$ respectively of $\Delta \mathrm{ABC}$ such that $\operatorname{ar}(\mathrm{DBC})=\operatorname{ar}(\mathrm{EBC})$. Prove that $\mathrm{DE} \| \mathrm{BC}$.

Q8. $\mathrm{XY}$ is a line parallel to side $\mathrm{BC}$ of a triangle $\mathrm{ABC}$. If $\mathrm{BE} \| \mathrm{AC}$ and $\mathrm{CF} \| \mathrm{AB}$ meet $\mathrm{XY}$ at $\mathrm{E}$ and $F$ respectively, show that ar $(\Delta \mathrm{ABE})=$ ar $(\Delta \mathrm{ACF})$.

Q9. The side $A B$ of a parallelogram $A B C D$ is produced to any point $P$. A line through A and parallel to CP meets CB produced at $\mathrm{Q}$ and then parallelogram $\mathrm{PBQR}$ is completed Show that ar $(\mathrm{ABCD})=\operatorname{ar}(\mathrm{PBQR}) .$

Q10. Diagonals AC and BD of a trapezium $\mathrm{ABCD}$ with $\mathrm{AB} \| \mathrm{DC}$ intersect each other at $\mathrm{O}$. Prove that ar $(\mathrm{AOD})=\operatorname{ar}(\mathrm{BOC})$.

Q11. In fig, $\mathrm{ABCDE}$ is a pentagon. A line through B parallel to

AC meets DC produced at $\mathrm{F}$. Show that
(i) $\operatorname{ar}(\mathrm{ACB})=\operatorname{ar}(\mathrm{ACF})$
(ii) $\operatorname{ar}(\mathrm{AEDF})=\operatorname{ar}(\mathrm{ABCDE})$

Q12. A villager Itwaari has a plot of land of the shape of a quadrilateral. The Gram Panchayat of the village decided to take over some portion of his plot from one of the corners to construct a Health Centre. Itwaari agrees to the above proposal with the condition that he should be given equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how this proposal will be implemented.

Q13. $\mathrm{ABCD}$ is a trapezium with $\mathrm{AB} \| \mathrm{DC}$. A line parallel to $\mathrm{AC}$ intersects $\mathrm{AB}$ at $\mathrm{X}$ and $\mathrm{BC}$ at $\mathrm{Y}$. Prove that ar $(\mathrm{ADX})=\operatorname{ar}(\mathrm{ACY})$.

Q14. In fig, $\mathrm{AP}\|\mathrm{BQ}\| \mathrm{CR}$. Prove that ar $(\mathrm{AQC})=\operatorname{ar}(\mathrm{PBR})$.

Q15. Diagonals $\mathrm{AC}$ and $\mathrm{BD}$ of a quadrilateral $\mathrm{ABCD}$ intersect at $\mathrm{O}$ in such a way that ar $(\mathrm{AOD})=\operatorname{ar}(\mathrm{BOC})$. Prove that $\mathrm{ABCD}$ is a trapezium.

Q16. In fig, ar $(\mathrm{DRC})=\operatorname{ar}(\mathrm{DPC})$ and ar $(\mathrm{BDP})=\operatorname{ar}(\mathrm{ARC})$. Show that both the quadrilaterals $\mathrm{ABCD}$ and DCPR are trapeziums.

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Q1. In fig, $\mathrm{ABCD}$ is a parallelogram, $\mathrm{AE} \perp \mathrm{DC}$ and $\mathrm{CF} \perp \mathrm{AD}$. If $\mathrm{AB}=16 \mathrm{~cm}, \mathrm{AE}=8 \mathrm{~cm}$ and $\mathrm{CF}=10 \mathrm{~cm}$, find $\mathrm{AD}$.

Q2. If $\mathrm{E}, \mathrm{F}, \mathrm{G}$ and $\mathrm{H}$ are respectively the mid-points of the sides of a parallelogram $\mathrm{ABCD}$, show that ar (EFGH) $=\frac{1}{2}$ ar $(\mathrm{ABCD})$.

Q3. $\mathrm{P}$ and $\mathrm{Q}$ are any two points lying on the sides $\mathrm{DC}$ and $\mathrm{AD}$ respectively of a parallelogram $\mathrm{ABCD}$. Show that ar $(\mathrm{APB})=\operatorname{ar}(\mathrm{BQC})$.

Q4. In figure, $\mathrm{P}$ is point in interior of a parallelogram $\mathrm{ABCD}$. Show that:
(i) ar ( $\triangle \mathrm{APB})+\operatorname{ar}(\triangle \mathrm{PCD})$
$=\frac{1}{2} \operatorname{ar}\left(\|^{\mathrm{gm}} \mathrm{ABCD}\right)$
(ii) ar ( $\triangle \mathrm{APD})+$ ar $(\Delta \mathrm{PBC})$
$=\operatorname{ar}(\Delta \mathrm{APB})+\operatorname{ar}(\Delta \mathrm{PCD})$

Q5. In fig, PQRS and ABRS are parallelograms and $\mathrm{X}$ is any point on side BR. Show that:
(i) $\operatorname{ar}(\mathrm{PQRS})=\operatorname{ar}(\mathrm{ABRS})$
(ii) $\operatorname{ar}(\mathrm{AX} \mathrm{S})=\frac{1}{2}$ ar $(\mathrm{PQRS})$

Q6. A farmer was having a field in the form of a parallelogram PQRS. She took any point A on RS and joined it to points $\mathrm{P}$ and $\mathrm{Q} .$ In how many parts the fields is divided? What are the shapes of these parts? The farmer wants to sow wheat and pulses in equal portions of the field separately. How should she do it?

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All Questions of Chapter 9 Exercise 9.1

Once you complete the chapter 9 then you can revise Ex. 9.1 by solving following questions

Q1. Which of the following figures lie on the same base and between the same parallels. In such a case, write the common base and the two parallels.

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All Questions of Chapter 8 Exercise 8.2

Once you complete the chapter 8 then you can revise Ex. 8.2 by solving following questions

Q1. $\quad \mathrm{ABCD}$ is a quadrilateral in which $\mathrm{P}, \mathrm{Q}, \mathrm{R}$ and $\mathrm{S}$ are mid points of the sides $\mathrm{AB}, \mathrm{BC}, \mathrm{CD}$ and DA (fig.) $\mathrm{AC}$ is a diagonal. Show that
(i) $\mathrm{SR} \| \mathrm{AC}$ and $\mathrm{SR}=1 / 2 \mathrm{C}$
(ii) $\mathrm{PQ}=\mathrm{SR}$
(iii) PQRS is a parallelogram.

Q2. $\mathrm{ABCD}$ is a rhombus and $\mathrm{P}, \mathrm{Q}, \mathrm{R}$ and $\mathrm{S}$ are the mid points of sides $\mathrm{AB}, \mathrm{BC}, \mathrm{CD}$ and $\mathrm{DA}$ respectively. Show that the quadrilateral PQRS is a rectangle.

Q3. $\mathrm{ABCD}$ is a rectangle and $\mathrm{P}, \mathrm{Q}, \mathrm{R}$ and $\mathrm{S}$ are mid-points of the sides $\mathrm{AB}, \mathrm{BC}, \mathrm{CD}$ and $\mathrm{DA}$ respectively. Show that the quadrilateral PQRS is a rhombus.

Q4. $\mathrm{ABCD}$ is a trapezium in which $\mathrm{AB} \| \mathrm{DC}, \mathrm{BD}$ is a diagonal and $\mathrm{E}$ is the mid-point of $\mathrm{AD}$. A line is drawn through $\mathrm{E}$ parallel to $\mathrm{AB}$ intersecting $\mathrm{BC}$ at $\mathrm{F}$ (fig.). Show that $\mathrm{F}$ is the mid-point of $\mathrm{BC}$.

Q5. In a parallelogram $\mathrm{ABCD}, \mathrm{E}$ and $\mathrm{F}$ are the mid-points of sides $\mathrm{AB}$ and $\mathrm{CD}$ respectively (fig.). Show that the line segments $\mathrm{AF}$ and EC trisect the diagonal $\mathrm{BD}$.

Q6. Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

Q7. $\mathrm{ABC}$ is a triangle right angled at $\mathrm{C}$. A line through the mid-point $\mathrm{M}$ of hypotenuse $\mathrm{AB}$ and parallel to BC intersects $\mathrm{AC}$ at $\mathrm{D}$. Show that
(i) $\mathrm{D}$ is the mid-point of $\mathrm{AC}$
(ii) $\mathrm{MD} \perp \mathrm{AC}$
(iii) $\mathrm{CM}=\mathrm{MA}=1 / 2 \mathrm{AB}$

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In this article, we have listed NCERT Solutions for Class 9 Maths chapter 8 Exercise 8.1 that you can download to start your preparations anytime.

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All Questions of Chapter 8 Exercise 8.1

Once you complete the chapter 8 then you can revise Ex. 8.1 by solving following questions

Q1. The angles of quadrilateral are in the ratio $3: 5: 9: 13$. Find all the angles of the quadrilateral.

Q2. If the diagonals of a parallelogram are equal, then show that it is a rectangle.

Q3. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Q4. Show that the diagonals of a square are equal and bisect each other at right angles.

Q5. Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

Q6. In figure, $\mathrm{ABCD}$ is a parallelogram. Diagonal AC bisects $\angle \mathrm{A}$. Show that
(i) it bisects $\angle \mathrm{C}$ also
(ii) $\mathrm{ABCD}$ is a rhombus.

Q7. $\mathrm{ABCD}$ is a rhombus. Show that diagonal $\mathrm{AC}$ bisects $\angle \mathrm{A}$ as well as $\angle \mathrm{C}$ and diagonal $\mathrm{BD}$ bisects $\angle \mathrm{B}$ as well as $\angle \mathrm{D}$.

Q8. $\mathrm{ABCD}$ is a rectangle in which diagonal AC bisects $\angle \mathrm{A}$ as well as $\angle \mathrm{C}$. Show that
(i) $\mathrm{ABCD}$ is a square
(ii) diagonal BD bisects $\angle \mathrm{B}$ as well as $\angle \mathrm{D}$.

Q9. In parallelogram $\mathrm{ABCD}$, two points $\mathrm{P}$ and $\mathrm{Q}$ are taken on diagonal $\mathrm{BD}$ such that $\mathrm{DP}=\mathrm{BQ}$. Show that :
(i) $\triangle \mathrm{APD} \cong \Delta \mathrm{CQB}$
(ii) $\mathrm{AP}=\mathrm{CQ}$
(iii) $\triangle \mathrm{AQB} \cong \Delta \mathrm{CPD}$
(iv) $\mathrm{AQ}=\mathrm{CP}$
(v) APCQ is a parallelogram

Q10. $\mathrm{ABCD}$ is a parallelogram and $\mathrm{AP}$ and $\mathrm{CQ}$ are perpendiculars from vertices $\mathrm{A}$ and $\mathrm{C}$ on diagonal BD. Show that
(i) $\triangle \mathrm{APB} \cong \Delta \mathrm{CQD}$
(ii) $\mathrm{AP}=\mathrm{CQ}$

Q11. In $\triangle \mathrm{ABC}$ and $\triangle \mathrm{DEF}, \mathrm{AB}=\mathrm{DE}, \mathrm{AB} \| \mathrm{DE}, \mathrm{BC}=\mathrm{EF}$ and $\mathrm{BC} \| \mathrm{EF}$. Vertices $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are joined to vertices $\mathrm{D}, \mathrm{E}$ and $\mathrm{F}$ respectively. Show that :
(i) quadrilateral ABED is a parallelogram
(ii) quadrilateral BEFC is a parallelogram
(iii) $\mathrm{AD} \| \mathrm{CF}$ and $\mathrm{AD}=\mathrm{CF}$
(iv) quadrilateral ACFD is a parallelogram
(v) $\mathrm{AC}=\mathrm{DF}$
(vi) $\triangle \mathrm{ABC} \cong \Delta \mathrm{DEF}$

Q12. $\mathrm{ABCD}$ is a trapezium in which $\mathrm{AB} \| \mathrm{CD}$ and $\mathrm{AD}=\mathrm{BC}$. Show that (fig)
(i) $\angle \mathrm{A}=\angle \mathrm{B}$
(ii) $\angle \mathrm{C}=\angle \mathrm{D}$
(iii) $\Delta \mathrm{ABC} \cong \Delta \mathrm{BAD}$
(iv) diagonal $\mathrm{AC}=$ diagonal $\mathrm{BD}$

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All Questions of Chapter 7 Exercise 7.4

Once you complete the chapter 7 then you can revise Ex. 7.4 by solving following questions

Q1. Show that in a right angled triangle, the hypotenuse is the longest side.

Q2. In figure, sides $\mathrm{AB}$ and $\mathrm{AC}$ of $\Delta \mathrm{ABC}$ are extended to points $\mathrm{P}$ and $\mathrm{Q}$ respectively. Also, $\angle \mathrm{PBC}<\angle \mathrm{QCB}$. Show that $\mathrm{AC}>\mathrm{AB}$

Q3. In fig, $\angle \mathrm{B}<\angle \mathrm{A}$ and $\angle \mathrm{C}<\angle \mathrm{D}$. Show that $\mathrm{AD}<\mathrm{BC}$.

Q4. $\mathrm{AB}$ and $\mathrm{CD}$ are respectively the smallest and longest sides of a quadrilateral $\mathrm{ABCD}$ (see figure). Show that $\angle \mathrm{A}>\angle \mathrm{C}$ and $\angle \mathrm{B}>\angle \mathrm{D}$.

Q5. In figure, $\mathrm{PR}>\mathrm{PQ}$ and $\mathrm{PS}$ bisects $\angle \mathrm{QPR}$. Prove that $\angle \mathrm{PSR}>\angle \mathrm{PSQ}$.

Q6. Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.

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NCERT Solutions for Class 9 Maths chapter 7 Exercise 7.3 – Triangles
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Here we have listed Class 9 maths chapter 7 exercise 7.3 solutions in PDF that is prepared by Kota’s top IITian’s Faculties by keeping Simplicity in mind.

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In this article, we have listed NCERT Solutions for Class 9 Maths chapter 7 Exercise 7.3 that you can download to start your preparations anytime.

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Download The PDF of NCERT Solutions for Class 9 Maths chapter 7 Exercise 7.3 “Triangles”

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All Questions of Chapter 7 Exercise 7.3

Once you complete the chapter 7 then you can revise Ex. 7.3 by solving following questions

Q1. $\triangle \mathrm{ABC}$ and $\Delta \mathrm{DBC}$ are two isosceles triangles on the same base $\mathrm{BC}$ and vertices $\mathrm{A}$ and $\mathrm{D}$ are on the same side of $\mathrm{BC}$ (see figure). If $\mathrm{AD}$ is extended to intersect $\mathrm{BC}$ at $\mathrm{P}$, show that

(i) $\triangle \mathrm{ABD} \cong \triangle \mathrm{ACD}$
(ii) $\triangle \mathrm{ABP} \cong \triangle \mathrm{ACP}$
(iii) AP bisects $\angle \mathrm{A}$ as well as $\angle \mathrm{D}$
(iv) AP is the perpendicular bisector of $\mathrm{BC}$.

Q2. $\mathrm{AD}$ is an altitude of an isosceles triangle $\mathrm{ABC}$ in which $\mathrm{AB}=\mathrm{AC}$. Show that
(i) AD bisects $\mathrm{BC}$
(ii) AD bisects $\angle \mathrm{A}$

Q3. Two sides $\mathrm{AB}$ and $\mathrm{BC}$ and median $\mathrm{AM}$ of one triangle $\mathrm{ABC}$ are respectively equal to side $\mathrm{PQ}$ and QR and median PN of $\Delta \mathrm{PQR}$ (see figure). Show that :
(i) $\Delta \mathrm{ABM} \cong \Delta \mathrm{PQN}$
(ii) $\Delta \mathrm{ABC} \cong \Delta \mathrm{PQR}$

Q4. BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.

Q5. $\mathrm{ABC}$ is an isosceles triangle with $\mathrm{AB}=\mathrm{AC}$. Draw $\mathrm{AP} \perp \mathrm{BC}$ to show that $\angle \mathrm{B}=\angle \mathrm{C}$

Class 9 NCERT Maths Book Chapterwise PDF

Class 9 NCERT Maths Exemplar Chapterwise PDF

Complete Solutions for Class 9 chapter 7

Class 9 Maths Chapter 6 Exercise 6.1 Solutions Free

Class 9 Maths Chapter 6 Exercise 6.2 Solutions Free

Class 9 Maths Chapter 6 Exercise 6.3 Solutions Free

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