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The curved surface area of cylinder X is 45% of the curved surface area of cylinder Y. If the volume of cylinder X is 27% of the volume of cylinder Y, then the height of cylinder X is what percentage of the height of cylinder Y?

The curved surface area of cylinder X is 45% of the curved surface area of cylinder Y. If the volume of cylinder X is 27% of the volume of cylinder Y, then the height of cylinder X is what percentage of the height of cylinder Y? Correct Answer 75%

Let the radius and height of cylinder X be ‘r’ units and ‘h’ units respectively

Let the radius and height of cylinder Y be ‘R’ units and ‘H’ units respectively

Given,

Curved surface area of cylinder X = 45% of Curved surface area of cylinder Y

⇒ 2πrh = (9/20) × (2πRH)

⇒ rh/RH = 9/20      ---(1)

Also,

Volume of cylinder X = 27% of Volume of cylinder Y

⇒ πr2h = (27/100) × (πR2H)

⇒ r2h/R2H = 27/100

Substituting from (1),

⇒ (r/R) × 9/20 = 27/100

⇒ r/R = 3/5

Substituting in (1),

⇒ (h/H) × 3/5 = 9/20

⇒ h/H = 3/4

⇒ h = (3/4) H

⇒ h = 75% of H

∴ Height of cylinder X is 75% of the height of cylinder Y

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