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The volume of a sphere of diameter 2p cm is given by

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π p^{2} c m^{3}

π p^{3} c m^{3}

4 π p^{2} c m^{3}

\frac{4}{3} π p^{3} c m^{3}

answer is D.

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Detailed Solution

Given the diameter of the sphere is 2p cm.
Radius =

D 2

So, the radius of sphere=

\frac{2 p}{2} = p cm

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.
Then, the volume of sphere, V

= \frac{4}{3} π (p)^{3}

\Rightarrow V = \frac{4}{3} π p^{3} c m^{3}

Therefore, the volume of a sphere of diameter 2p cm is

\frac{4}{3} π p^{3} c m^{3} .

Hence option (4) is correct.

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