Find the volume of a sphere whose surface area is 154 cm2.
Question.

Find the volume of a sphere whose surface area is $154 \mathrm{~cm}^{2} .\left[\right.$ Assume $\left.\pi=\frac{22}{7}\right]$


Solution:

Let radius of sphere be r.

Surface area of sphere $=154 \mathrm{~cm}^{2}$

$\Rightarrow 4 \pi r^{2}=154 \mathrm{~cm}^{2}$

$\Rightarrow r^{2}=\left(\frac{154 \times 7}{4 \times 22}\right) \mathrm{cm}^{2}$

$\Rightarrow r=\left(\frac{7}{2}\right) \mathrm{cm}=3.5 \mathrm{~cm}$

Volume of sphere $=\frac{4}{3} \pi r^{3}$

$=\left[\frac{4}{3} \times \frac{22}{7} \times(3.5)^{3}\right] \mathrm{cm}^{3}$

$=179 \frac{2}{3} \mathrm{~cm}^{3}$

Therefore, the volume of the sphere is $179 \frac{2}{3} \mathrm{~cm}^{3}$.
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