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Q.

If the surface area of a sphere is $36 π {cm}^{2}$ , then the volume of the sphere is equal to

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a

12 π {cm}^{3}

b

36 π {cm}^{3}

c

72 π {cm}^{3}

d

108 π {cm}^{3}

answer is B.

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Detailed Solution

Given that, the surface area of sphere

= 36 π c m^{2}

.
The formula for the surface area of sphere is given by,
Surface area of sphere

= 4 π r^{2},

where r is its radius.
So,

4 π r^{2} = 36 π

{\Rightarrow r}^{2} = 9

\Rightarrow r = 3 cm

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

= \frac{4}{3} π r^{3}

So, after substituting the value of all the dimensions in the formula we get,

V = \frac{4}{3} π \times 3^{3}

\Rightarrow V = 4 \times π \times 9

\Rightarrow V = 36 π c m^{3}

Therefore, the volume of sphere is

36 π c m^{3} .

Hence option (2) is correct.

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If the surface area of a sphere is 36πcm2, then the volume of the sphere is equal to