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If the surface area of a sphere is $324 π c m 2$ then its volume is

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950 π

c m^{3}

972 π

c m^{3}

975 π

c m^{3}

980 π

c m^{3}

answer is B.

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Detailed Solution

Given the surface area of sphere is

324 πc m^{2}

.
Surface area of sphere is given by

4 π r 2

⇒ 4 π r 2 = 324 π ⇒ r 2 = 81 ⇒ r = 9 c m

The formula for the volume of sphere is given by,
Volume of a sphere

= \frac{4}{3} π r^{3}

, where

r

is the radius.
So, after substituting the value of all the dimensions in the formula we get,
Volume of sphere, V =

\frac{4}{3} π (9)^{3}

\Rightarrow V = \frac{4}{3} \times π \times 729

\Rightarrow V = 972 πc m^{3}

Therefore, the volume of sphere is

972 π

c m^{3}

.
Hence option (2) is correct.

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