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What will be the volume of a cylinder having its total surface area as $462 c m 2$ and its curved surface area equal to one-third its total surface area?

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630

c m 3

539

c m 3

540

c m 3

670

c m 3

answer is B.

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Detailed Solution

It is given that the total surface area of the cylinder is,

2 π r r + h = 462 cm 2 .

And the curved surface area is one-third of the total surface area of the cylinder.

⇒ 2 π r h = 13 × 462 ⇒ 2 π r h = 154 cm 2 ................ (1)

The ratio of total surface area to curved surface area will be given as,

2 π r r + h 2 π r h = 462154 ⇒ r + h h = 3 ⇒ r + h = 3 h ⇒ r = 2 h

⇒ r = 2 h ⇒ h = r 2

Substituting

h = r 2

in (1), we get,

2 π r × r 2 = 154 ⇒ π r 2 = 154 ⇒ 227 × r 2 = 154 ⇒ r 2 = 154 × 722

⇒ r 2 = 49 ⇒ r = 7 cm and h = 72 cm

Now, we can calculate the volume of the cylinder as,
Question Image

Therefore the volume of the cylinder is

539 cm 3 .

Hence, option (2) is correct.

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