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If the surface area of sphere is $(144 π) m^{2}$ , then its volume is

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(288 π) m^{3}

(188 π) m^{3}

(300 π) m^{3}

(316 π) m^{3}

answer is A.

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Detailed Solution

Given that, the surface area of sphere =

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

4 π r^{2} = 144 π

\Rightarrow r = \sqrt{\frac{144}{4}}

\Rightarrow r = \sqrt{{(\frac{12}{2})}^{2}}

\Rightarrow r = 6 m

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 = 43 × π × 63 ⇒ V = 2800 m 3

Therefore, the volume of sphere is

288 π m^{3} .

Hence option (1) is correct.

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