Question

Find the volumes of a sphere whose surface area is $154c{m}^2$.

Answer 1

Given :
Surface area of sphere $=154c{m}^2$
We know that the Surface area of sphere is given by $4\pi r^2$

$154=4\times \frac{22}{7}\times r^2$

$\Rightarrow 154\times 7=88r^2$

$\Rightarrow r^2=\frac{154\times 7}{88}$

$\Rightarrow r^2=\frac{7\times 7}{4}$

$\Rightarrow r^2=\frac{49}{4}$

$\Rightarrow r=\sqrt{\frac{49}{4}}=\frac{7}{2}$

$\Rightarrow r=\frac{7}{2}cm$

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

$=\frac{4}{3}\times \frac{22}{7}\times (\frac{7}{2}{)}^3$

$=\frac{4}{3}\times \frac{22}{7}\times \left(\frac{7}{2}\right)\times \left(\frac{7}{2}\right)\times \left(\frac{7}{2}\right)$

$=\frac{22\times 7\times 7}{3\times 2}$

$=\frac{11\times 49}{3}=\frac{539}{3}=179.66c{m}^3$

Hence, the Volume of Sphere is $179.66c{m}^3$.