Question

a cube and cuboid have the same volume the dimension of the cuboid are in the ratio of 1 ratio 2 ratio 4 if the difference between the cost of polishing the cuboid and that you were @ rupees 5 per metre square is rupees 80 find the edge of the cube

Answer 1

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Here your answer
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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
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20k2 = 80 ⇒ k2 = 4 ⇒ k = 2

∴ Volume of the cube = 8k3 = 8(2)3
= 64 m3

= volume of the cuboid.

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