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The ratio of volumes of two cubes X and Y is ratio 8 ∶ 3. If the total surface area of cube X is increased by 44% and that of cube Y is decreased by 36%, then what is the ratio of the new volume of the cube X to that of cube Y?

The ratio of volumes of two cubes X and Y is ratio 8 ∶ 3. If the total surface area of cube X is increased by 44% and that of cube Y is decreased by 36%, then what is the ratio of the new volume of the cube X to that of cube Y? Correct Answer 9 ∶ 1

Given:

Ratio of volumes of two cubes X and Y is ratio 8 ∶ 3

Total surface area of cube X is increased by 44% and that of cube Y is decreased by 36%,

Formula used:

Volume of cube = (side)3

Calculation:

Considering cube X,

The surface area of cube X is increased by 44%,

⇒ Ratio of final to initial surface area of cube X = (100 + 44)/100 = 144/100 = 36/25

As we know, total surface area of cube is directly proportional to square of edge length,

⇒ Ratio of final to initial edge length of cube X = √(36/25) = 6/5 

Also, volume of cube is directly proportional to cube of edge length,

⇒ Ratio of final to initial volume of cube X = (6/5)3 = 216/125      ----(1)

Similarly,

Considering cube Y,

The surface area of cube Y is decreased by 36%,

⇒ Ratio of final to initial surface area of cube Y = (100 – 36)/100 = 64/100 = 16/25

⇒ Ratio of final to initial edge length of cube Y = √(16/25) = 4/5

⇒ Ratio of final to initial volume of cube Y = (4/5)3 = 64/125      ----(2)

Now,

Dividing (1) by (2), we get,

⇒ Ratio of final volumes of cube X to cube Y/Ratio of initial volumes of cube X to cube Y = 216/64 = 27/8

∵ Ratio of initial volumes of cube X to cube Y = 4/9

⇒ Ratio of final volumes of cube X to cube Y = 27/8 × 8/3 = 9

∴ Ratio of final volume of cube X to that of cube Y = 9 ∶ 1

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