It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep.
[question] Question. It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel $10 \mathrm{~m}$ deep. If the cost of painting is at the rate of Rs 20 per $\mathrm{m}^{2}$, find (i) Inner curved surface area of the vessel (ii) Radius of the base (iii) Capacity of the vessel Assume $\left.\pi=\frac{22}{7}\right]$ [/question] [solution] Solution: (i) Rs 20 is the cost of painting $1 \mathrm{~m}^{2}$ area. Rs 2200 is the cost of painting $=\left(\frac{1}{20} \times 2200\right) \math...
Read More →If the lateral surface of a cylinder is $94.2 \mathrm{~cm}^{2}$
[question] Question. If the lateral surface of a cylinder is $94.2 \mathrm{~cm}^{2}$ and its height is $5 \mathrm{~cm}$, then find (i) radius of its base (ii) its volume. [Use $\pi=3.14]$ [/question] [solution] Solution: (i) Height $(h)$ of cylinder $=5 \mathrm{~cm}$ Let radius of cylinder be r. CSA of cylinder $=94.2 \mathrm{~cm}^{2}$ $2 \pi r h=94.2 \mathrm{~cm}^{2}$ $(2 \times 3.14 \times r \times 5) \mathrm{cm}=94.2 \mathrm{~cm}^{2}$ $r=3 \mathrm{~cm}$ (ii) Volume of cylinder $=\pi r^{2} h$ ...
Read More →The circumference of the base of cylindrical vessel is 132 cm and its height is 25 cm.
[question] Question. The circumference of the base of cylindrical vessel is $132 \mathrm{~cm}$ and its height is $25 \mathrm{~cm}$. How many litres of water can it hold? (1000 cm $^{3}=1 /$ ) $\left[\right.$ Assume $\left.\pi=\frac{22}{7}\right]$ [/question] [solution] Solution: Let the radius of the cylindrical vessel be r. Height (h) of vessel = 25 cm Circumference of vessel $=132 \mathrm{~cm}$ $2 \pi r=132 \mathrm{~cm}$ $r=\left(\frac{132 \times 7}{2 \times 22}\right) \mathrm{cm}=21 \mathrm{~...
Read More →A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour.
[question] Question. A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute? [/question] [solution] Solution: Rate of water flow = 2 km per hour $=\left(\frac{2000}{60}\right) \mathrm{m} / \mathrm{min}$ $=\left(\frac{100}{3}\right) \mathrm{m} / \mathrm{min}$ Depth (h) of river = 3 m Width (b) of river = 40 m Volume of water flowed in $1 \mathrm{~min}=\left(\frac{100}{3} \times 40 \times 3\right) \mathrm{m}^{3}=4000 \mathrm{~m}^{3...
Read More →A solid cube of side 12 cm is cut into eight cubes of equal volume.
[question] Question. A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas. [/question] [solution] Solution: Side (a) of cube = 12 cm Volume of cube $=(a)^{3}=(12 \mathrm{~cm})^{3}=1728 \mathrm{~cm}^{3}$ Let the side of the smaller cube be $a_{1}$. Volume of 1 smaller cube $=\left(\frac{1728}{8}\right) \mathrm{cm}^{3}=216 \mathrm{~cm}^{3}$ $\left(a_{1}\right)^{3}=216 \mathrm{~cm}^{3}$ $\Rightarr...
Read More →A godown measures 40 m × 25 m × 15 m.
[question] Question. A godown measures $40 \mathrm{~m} \times 25 \mathrm{~m} \times 15 \mathrm{~m}$. Find the maximum number of wooden crates each measuring $1.5 \mathrm{~m} \times 1.25 \mathrm{~m} \times 0.5 \mathrm{~m}$ that can be stored in the godown. [/question] [solution] Solution: The godown has its length $\left(l_{1}\right)$ as $40 \mathrm{~m}$, breadth $\left(b_{1}\right)$ as $25 \mathrm{~m}$, height $\left(h_{1}\right)$ as $15 \mathrm{~m}$, while the wooden crate has its length $\left...
Read More →A village, having a population of 4000,
[question] Question. A village, having a population of 4000 , requires 150 litres of water per head per day. It has a tank measuring $20 \mathrm{~m} \times 15 \mathrm{~m} \times 6 \mathrm{~m}$. For how many days will the water of this tank last? [/question] [solution] Solution: The given tank is cuboidal in shape having its length (l) as 20 m, breadth (b) as 15 m, and height (h) as 6 m. Capacity of tank $=1 \times b \times h$ $=(20 \times 15 \times 6) \mathrm{m}^{3}=1800 \mathrm{~m}^{3}=1800000$...
Read More →The capacity of a cuboidal tank is 50000 litres of water.
[question] Question. The capacity of a cuboidal tank is 50000 litres of water. Find the breadth of the tank, if its length and depth are respectively 2.5 m and 10 m. [/question] [solution] Solution: Let the breadth of the tank be b m. Length (l) and depth (h) of tank is 2.5 m and 10 m respectively. Volume of $\operatorname{tank}=1 \times b \times h$ $=(2.5 \times b \times 10) \mathrm{m}^{3}$ $=25 b \mathrm{~m}^{3}$ Capacity of tank $=25 b \mathrm{~m}^{3}=25000 \mathrm{~b}$ litres $\therefore 250...
Read More →Find the cost of digging a cuboidal pit 8 m long,
[question] Question. Find the cost of digging a cuboidal pit $8 \mathrm{~m}$ long, $6 \mathrm{~m}$ broad and $3 \mathrm{~m}$ deep at the rate of Rs 30 per $\mathrm{m}^{3}$. [/question] [solution] Solution: The given cuboidal pit has its length $(l)$ as $8 \mathrm{~m}$, width $(b)$ as $6 \mathrm{~m}$, and depth $(h)$ as $3 \mathrm{~m}$. Volume of pit $=1 \times b \times h$ $=(8 \times 6 \times 3) \mathrm{m}^{3}=144 \mathrm{~m}^{3}$ Cost of digging per $\mathrm{m}^{3}$ volume $=$ Rs 30 Cost of dig...
Read More →What type of clothes should we wear in summer?
[question] Question What type of clothes should we wear in summer? [/question] [solution] Solution We should wear light colored cotton clothes in summer. Light color because it reflects heat. Cotton clothes because it has pores in it, which absorbs sweat and allows the sweat to evaporate faster thereby giving cooling effect. [/solution]...
Read More →A cuboidal vessel is 10 m long and 8 m wide.
[question] Question. A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid? [/question] [solution] Solution: Let the height of the cuboidal vessel be h. Length (l) of vessel = 10 m Width (b) of vessel = 8 m Volume of vessel $=380 \mathrm{~m}^{3}$ $\therefore / \times b \times h=380$ $[(10)(8) h] \mathrm{m}^{2}=380 \mathrm{~m}^{3}$ $h=4.75 \mathrm{~m}$ Therefore, the height of the vessel should be 4.75 m. [/solution]...
Read More →A cuboidal water tank is 6 m long,
[question] Question. A cuboidal water tank is $6 \mathrm{~m}$ long, $5 \mathrm{~m}$ wide and $4.5 \mathrm{~m}$ deep. How many litres of water can it hold? $\left(1 \mathrm{~m}^{3}=1000 /\right)$ [/question] [solution] Solution: The given cuboidal water tank has its length $(l)$ as $6 \mathrm{~m}$, breadth $(b)$ as $5 \mathrm{~m}$, and height $(h)$ as $4.5 \mathrm{~m}$. Volume of tank $=l \times b \times h$ $=(6 \times 5 \times 4.5) \mathrm{m}^{3}=135 \mathrm{~m}^{3}$ Amount of water that 1 m3 vo...
Read More →A matchbox measures $4 \mathrm{~cm} \times 2.5 \mathrm{~cm} \times 1.5 \mathrm{~cm}$.
[question] Question. A matchbox measures $4 \mathrm{~cm} \times 2.5 \mathrm{~cm} \times 1.5 \mathrm{~cm}$. What will be the volume of a packet containing 12 such boxes? [solution] Solution: Matchbox is a cuboid having its length $(l)$, breadth $(b)$, height $(h)$ as $4 \mathrm{~cm}, 2.5 \mathrm{~cm}$, and $1.5 \mathrm{~cm}$. Volume of 1 match box $=1 \times b \times h$ $=(4 \times 2.5 \times 1.5) \mathrm{cm}^{3}=15 \mathrm{~cm}^{3}$ Volume of 12 such matchboxes $=(15 \times 12) \mathrm{cm}^{3}$ ...
Read More →A right circular cylinder just encloses a sphere of radius r (see figure).
[question] Question. A right circular cylinder just encloses a sphere of radius r (see figure). Find (i) surface area of the sphere, (ii) curved surface area of the cylinder, (iii) ratio of the areas obtained in (i) and (ii). [/question] [solution] Solution: (i) Surface area of sphere $=4 \pi r^{2}$ (ii) Height of cylinder $=r+r=2 r$ Radius of cylinder $=r$ CSA of cylinder $=2 \pi r h$ $=2 \pi r(2 r)$ $=4 \pi r^{2}$ (iii) Required ratio $=\frac{\text { Surface area of sphere }}{\text { CSA of cy...
Read More →A hemispherical bowl is made of steel, 0.25 cm thick.
[question] Question. 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. $\left[\right.$ Assume $\left.\pi=\frac{22}{7}\right]$ [/question] [solution] Solution: Inner radius of hemispherical bowl = 5 cm Thickness of the bowl = 0.25 cm $\therefore$ Outer radius $(r)$ of hemispherical bowl $=(5+0.25) \mathrm{cm}$ $=5.25 \mathrm{~cm}$ Outer CSA of hemispherical bowl $=2 \pi r^{2}$ $=2 \ti...
Read More →The diameter of the moon is approximately one-fourth of the diameter of the earth.
[question] Question. The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface area. [/question] [solution] Solution: Let the diameter of earth be $d$. Therefore, the diameter of moon will be $\frac{d}{4}$. Radius of earth $=\frac{d}{2}$ Radius of moon $=\frac{1}{2} \times \frac{d}{4}=\frac{d}{8}$ Surface area of moon $=4 \pi\left(\frac{d}{8}\right)^{2}$ Surface area of earth $=4 \pi\left(\frac{d}{2}\right)^{2}$ Required ratio $=\frac{4 \p...
Read More →Why are we able to sip hot tea or milk faster from a saucer rather than a cup?
[question] Question Why are we able to sip hot tea or milk faster from a saucer rather than a cup? [/question] [solution] Solution Tea in a saucer has larger surface area than in a cup. The rate of evaporation is faster with increased surface area. The cooling of tea in saucer takes place sooner than in a cup. Hence we are able to sip hot tea or milk faster from a saucer rather than a cup. [/solution]...
Read More →Find the radius of a sphere whose surface area is $154 \mathrm{~cm}^{2}$
[question] Question. Find the radius of a sphere whose surface area is $154 \mathrm{~cm}^{2} .\left[\right.$ Assume $\left.\pi=\frac{22}{7}\right]$ [/question] [solution] Solution: Let the radius of the sphere be r. Surface area of sphere = 154 $\therefore 4 m r^{2}=154 \mathrm{~cm}^{2}$ $r^{2}=\left(\frac{154 \times 7}{4 \times 22}\right) \mathrm{cm}^{2}=\left(\frac{7 \times 7}{2 \times 2}\right) \mathrm{cm}^{2}$ $r=\left(\frac{7}{2}\right) \mathrm{cm}=3.5 \mathrm{~cm}$ Therefore, the radius of...
Read More →Why does our palm feel cold when we put some acetone or petrol or perfume on it?
[question] Question Why does our palm feel cold when we put some acetone or petrol or perfume on it? [/question] [solution] Solution Acetone, petrol or perfume evaporate when they come into contact with air. The evaporation causes cooling sensation in our hands. [/solution]...
Read More →A hemispherical bowl made of brass has inner diameter 10.5 cm.
[question] Question. 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 Rs 16 per $100 \mathrm{~cm}^{2} .\left[\right.$ Assume $\left.\pi=\frac{22}{7}\right]$ [/question] [solution] Solution: Inner radius $(r)$ of hemispherical bowl $=\left(\frac{10.5}{2}\right) \mathrm{cm}=5.25 \mathrm{~cm}$ Surface area of hemispherical bowl $=2 \pi r^{2}$ $=\left[2 \times \frac{22}{7} \times(5.25)^{2}\right] \mathrm{cm}^{2}$ ...
Read More →The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it.
[question] Question. 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. [/question] [solution] Solution: Radius (r1) of spherical balloon = 7 cm Radius (r2) of spherical balloon, when air is pumped into it = 14 cm Required ratio $=\frac{\text { Initial surface area }}{\text { Surface area after pumping air into balloon }}$ $=\frac{4 \pi r_{1}^{2}}{4 \pi r_{2}^{2}}=\left(\frac{r_{1}}{r_{2}...
Read More →Find the total surface area of a hemisphere of radius 10 cm.
[question] Question. Find the total surface area of a hemisphere of radius $10 \mathrm{~cm}$. [Use $\pi=3.14$ ] [/question] [solution] Solution: Radius (r) of hemisphere = 10 cm Total surface area of hemisphere = CSA of hemisphere + Area of circular end of hemisphere $=2 \pi r^{2}+\pi r^{2}$ $=3 \pi r^{2}$ $=\left[3 \times 3.14 \times(10)^{2}\right] \mathrm{cm}^{2}$ $=942 \mathrm{~cm}^{2}$ Therefore, the total surface area of such a hemisphere is $942 \mathrm{~cm}^{2}$. [/solution]...
Read More →How does the water kept in an earthen pot (matka) become cool during summer?
[question] Question How does the water kept in an earthen pot (matka) become cool during summer? [/question] [solution] Solution The earthen pot is porous with lot of pores on it, the water oozes out through these pores and the water gets evaporated at the surface of the pot thereby causing cooling effect. This makes the pot cold and the water inside the pot cools by this process. [/solution]...
Read More →Find the surface area of a sphere of diameter:
[question] Question. Find the surface area of a sphere of diameter: (i) $14 \mathrm{~cm}$ (ii) $21 \mathrm{~cm}$ (iii) $3.5 \mathrm{~m}$ [Assume $\left.\pi=\frac{22}{7}\right]$ [/question] [solution] Solution: (i) Radius $(r)$ of sphere $=\frac{\text { Diameter }}{2}=\left(\frac{14}{2}\right) \mathrm{cm}=7 \mathrm{~cm}$ Surface area of sphere $=4 \pi r^{2}$ $=\left(4 \times \frac{22}{7} \times(7)^{2}\right) \mathrm{cm}^{2}$ $=(88 \times 7) \mathrm{cm}^{2}$ $=616 \mathrm{~cm}^{2}$ Therefore, the ...
Read More →Why does a desert cooler cool better on a hot dry day?
[question] Question Why does a desert cooler cool better on a hot dry day? [/question] [solution] Solution The outer walls of the cooler get sprinkled by water constantly. This water evaporates due to hot dry weather. Evaporation causes cooling of inside air of cooler. This cool air is sent in the room by the fan. [/solution]...
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