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A solid cylinder has total surface area of 462 cm2. Its curved surface area is one third of its total surface area. Find the volume of the cylinder.

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Let r cm be the radius of the base and h cm be the height of the cylinder,

Then, total surface area of cylinder = 2πr (r + h)

Curved surface area of cylinder = 2πr

We have, 

Curved surface area = 1/3(Total surface area) = 1/3 x 462 cm2 = 154 cm2 

⇒  2πrh = 154 

Also, 2πrh + 2πr2 = 462    ⇒ 154 + 2πr2 = 462

⇒  2πr2 = 462 - 154 = 308 cm2

2 x 22/7 x r2 = 308

⇒  r= 308 x 7/2 x 22 = 72  ⇒  r = 7 cm

Again 2πrh = 154    ⇒ 2 x 22/7 x 7 x h = 154 

⇒ h = 154/2 x 22 = 7/2 cm 

Volume of the cylinder =  πr2h

= 22/7 x 7 x 7 x 7/2 = 539 cm3

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