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Probability

Question
CBSEENMA9003496
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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.

Solution

Let the dimensions of the cuboid be ft m, 2k m, 4k m. Then,
Volume of the cuboid
= (k) (2k) (4k) m3 = 8k3 m3
Volume of the cube = 8k3 m3
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 140k2
Difference 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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