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131. A cube and a cuboid have the same volume. The dimensions of the cuboid are in the ratio 1 : 2 : 4. If the difference between the cost of painting the cuboid and cube (whole surface area) at the rate of र 5/m² is र 80, find their volumes.

Let the dimensions of the cuboid be ft m, 2k m, 4k m. Then,
Volume of the cuboid
= (k) (2k) (4k) m³ = 8k³ m³Volume of the cube = 8k³ m^{3

$therefore$} Side of the cube = $left parenthesis 8 straight k cubed right parenthesis to the power of begin inline style 1 third end style end exponent space straight m equals 2 straight k space straight m$

Whole surface area of the cube = 6(2k)² m² = 24k² m² Page 240(2)
Whole surface area of the cuboid = 2 (lb + bh + hl)
= 2{k ⋅2k + 2k ⋅ 4k + 4k ⋅ k}
= 28k² m² Cost of painting the cube = (24k²) (5)
= र 120k² Cost of painting the cuboid = (28k²) (5)
= र 140k²Difference between the cost of painting the cuboid and cube
= र 140k² – र 120k² = र 20 k² According to the question,
20k² = 80 ⇒ k² = 4 ⇒ k = 2
∴ Volume of the cube = 8k³ = 8(2)³ = 64 m³= volume of the cuboid

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132. A teak wood is cut first in the form of a cuboid of length 2.3 m, width 0.75 m and of a certain thickness. Its volume is 1.104 m³. How many rectangular planks of size 1.104 m³, how many rectangular planks of size 2.3 m x 0.75 m x 0.04 m can be cut from the cuboid?

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133. The length of a cinema hall is 20 m and its width is 16 m. The sum of the areas of its floor and flat roof is equal to the surface area of its four walls. Find the volume and height of the hall.

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134. The length, breadth and height of a cuboid are 20 m, 24 m, 12 m respectively. The dimensions of length, breadth and depth are increased by 15%, 25% and 50% respectively. What is the ratio between the volume of the original cuboid and the new cuboid.

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135. A wall was to be built across an open ground to cover a width (or breadth) of 10 m. The height of the wall is 4 m and thickness of the wall is 24 cm. If this wall is to be built up with bricks whose dimensions are 24 cm x 12 cm x 8 cm, how many bricks would be required?

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136. A child playing with building blocks, which are of the shape of cubes, has built a structure as shown in figure. If the edge of each cube is 3 cm, find the volume of the structure built by the child.