Question

Find the volume of a sphere whose surface area is $154c{m}^2$. (Assume $\pi =\frac{22}{7}$)

Answer 1

Step $1$: Find the radius of the sphere based on given information

Given, the surface area $=4{\mathrm{\pi r}}^2$

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

$$\begin{gathered} r^2=\frac{154\times 7}{4\times 22} \\ {r}^2=\frac{49}{4} \end{gathered}$$

$r=\frac{7}{2}cm$ [ Taking the square root ]

Step $2$: Find the volume of a sphere

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

$$\begin{gathered} =\frac{4}{3}\times \frac{22}{7}\times {\left(\frac{7}{2}\right)}^3 \\ =\frac{4}{3}\times \frac{22}{7}\times 42.875‬ \\ =179.67c{m}^3 \end{gathered}$$

Hence, the volume of a sphere is $179.67c{m}^3$.