# If the ratio of curved surface area and total surface area of a cylinder is 1 : 3, then find the volume of cylinder when the height is 2 cm.

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If the ratio of curved surface area and total surface area of a cylinder is 1 : 3, then find the volume of cylinder when the height is 2 cm.

answered Nov 27, 2017 by (-3,089 points)

Let the radius and height of the cylinder be r and h, respectively .

Given that, Curved surface area / Total surface area = 1/3

⇒ 2πrh / 2πr(h + r) = 1/3 3h = h + r

⇒ r = 2h = 4cm

∴ volume of cylinder πr2h

= π × (4)× 2 = 32π cm

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