A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85cm (See figure 18.5). The thickness of the plank is 5cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per cm2. Find the total expenses required for polishing and painting the surface of the bookshelf.
External length of book shelf = 85 cm
Breadth = 25 cm
Height = 110 cm
External surface area of shelf while leaving front face of shelf
lh + 2(lb + bh)
[85 * 110 + 2(85 * 25 + 25 * 110)]
$19100 \mathrm{~cm}^{2}$
Area of Front face $=\left[85^{*} 110-75^{*} 100+2\left(75^{*} 5\right)\right] \mathrm{cm}^{2}$
$=1850+750 \mathrm{~cm}^{2}$
$=2600 \mathrm{~cm}^{2}$
Area to be polished $=19100+2600 \mathrm{~cm}^{2}$
$=21700 \mathrm{~cm}^{2}$
Cost of polishing $1 \mathrm{~cm}^{2}$ area $=$ Rs. $0.20$
Cost of polishing $21700 \mathrm{~cm}^{2}$ area $=21700 * 0.20$
= Rs. 4340
Now, Length (l), breadth (b), height ( $h$ ) of each row of book shelf is $75 \mathrm{~cm}, 20 \mathrm{~cm}$ and $30 \mathrm{~cm}=\left(\frac{110-20}{3}\right)$
respectively.
Area to be painted in 1 row = 2(l + h)b + lh
$[2(75+30) * 20+75 * 30)] \mathrm{cm}^{2}$
$(4200+2250) \mathrm{cm}^{2}$
$6450 \mathrm{~cm}^{2}$
Area to be painted in 3 rows = 3 * 6450
$=$ Rs. $19350 \mathrm{~cm}^{2}$
Cost of painting $1 \mathrm{~cm}^{2}$ area $=$ Rs. $0.10$
Cost of painting $19350 \mathrm{~cm}^{2}$ area $=19350 * 0.10$
= Rs.1935
Total expense required for polishing and painting the surface of the bookshelf = 4340 + 1935
= Rs.6275
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- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,