Question

The volume of a sphere is $3000\mathrm{\pi }{\mathrm{m}}^3$. What is the surface area of the sphere to the nearest square meter?

Answer 1

Step-1: Find the radius of the sphere:

Given that,

Volume $\left(\mathrm{V}\right)$ $=3000\mathrm{\pi }{\mathrm{m}}^3$

By using the formula, $\mathrm{V}=\frac{4}{3}{\mathrm{\pi r}}^3$, we get

$\begin{array}{rcl}\frac{4}{3}{\mathrm{\pi r}}^3& =& 3000\mathrm{\pi }\\ & \Rightarrow & {\mathrm{r}}^3=\frac{3000\times 3}{4}\\ & \Rightarrow & {\mathrm{r}}^3=2250\\ & \Rightarrow & \mathrm{r}={\left(2250\right)}^{\frac{1}{3}}\\ & \Rightarrow & =13.1\mathrm{m}\end{array}$

Step-2: Find the surface area:

The formula of the surface area $\left(\mathrm{S}\right)$ is $4{\mathrm{\pi r}}^2$.

By substituting the value of $\mathrm{r}$ in the above formula, we get

$\begin{array}{rcl}\mathrm{S}& =& 4\mathrm{\pi }{\left(13.1\right)}^2\\ & =& 4\times \frac{22}{7}\times 171.61\left[\because \pi =\frac{22}{7}\right]\\ & =& 2157.38{\mathrm{m}}^2\end{array}$

Hence, the surface area of the sphere is $2157.38{\mathrm{m}}^2$.