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In this question two quantities are given. Find and compare them and choose the appropriate options. A cylinder of radius R and height H has the same volume as that of a sphere of radius r. The surface area of sphere is more than the curved surface area of cylinder. Quantity I: x, where 9x – 2 = 0 Quantity II: R/H; where a cylinder of radius R and height H has the same volume as that of a sphere of radius r. The surface area of sphere is more than the curved surface area of cylinder.

In this question two quantities are given. Find and compare them and choose the appropriate options. A cylinder of radius R and height H has the same volume as that of a sphere of radius r. The surface area of sphere is more than the curved surface area of cylinder. Quantity I: x, where 9x – 2 = 0 Quantity II: R/H; where a cylinder of radius R and height H has the same volume as that of a sphere of radius r. The surface area of sphere is more than the curved surface area of cylinder. Correct Answer Quantity II > Quantity I

⇒ Quantity I: 9x – 2 = 0

⇒ x = 2/9

Quantity II:

⇒ Volume of cylinder = πR2H

⇒ Volume of sphere = 4/3πr3

Given that they are equal,

⇒ r = {3R2H/4}1/3

⇒ Surface area of sphere = 4πr2

⇒ CSA of cylinder = 2πRH

Given that surface area of sphere > CSA of cylinder

⇒ 4πr2 > 2πRH

⇒ r2/RH > 1/2

⇒ {3R2H/4}2/3/RH > 1/2

⇒ {3/4(R/H)0.5}2/3 > 1/2

Rearranging R/H > 2/9

∴ Quantity II > Quantity I

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