Find the volume of a sphere whose surface area is $ 154 \mathrm{~cm}^{2} $.

AcademicMathematicsNCERTClass 9

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 $179.67\ cm^3$.

raja
Updated on 10-Oct-2022 13:46:39

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