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Find the volume of a sphere whose surface area is \( 154 \mathrm{~cm}^{2} \).
Given:
The surface area of a sphere is $154\ cm^{2}$.
To do:
We have to find the volume of the sphere.
Solution:
Let $r$ be the radius of the sphere.
Therefore,
Surface area of the sphere$=4\pi r^2$
$=154$
This implies,
$r^2=\frac{154}{4\pi}$
$r^2=\frac{154}{4\times\frac{22}{7}}$
$r^2=\frac{154\times7}{4\times22}$
$r^2=\frac{49}{4}$
$r^2=\frac{7^2}{2^2}$
$r=\frac{7}{2}$
Volume of the sphere $=\frac{4}{3} \pi (\frac{7}{2})^{3}$
$=\frac{4}{3} \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times \frac{7}{2}$
$=\frac{11 \times 7 \times 7}{3}$
$=179.67 \mathrm{~cm}^{3}$
Therefore, the volume of the sphere is $179.67\ cm^3$.
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