Question

The radius of a sphere is $2r$, then its volume will be:

• A. $\frac{4}{3}{\mathrm{\pi r}}^3$
• B. $4{\mathrm{\pi r}}^3$
• C. $\frac{8}{3}{\mathrm{\pi r}}^3$
• D. $\frac{32}{3}{\mathrm{\pi r}}^3$

Answer 1

The correct option is D

$\frac{32}{3}{\mathrm{\pi r}}^3$

Find the volume of the sphere:

Given that, radius $\left(r\right)$ of the sphere $=2r$

The volume of the sphere of radius $\left(r\right)$ $=\frac{4}{3}{\mathrm{\pi r}}^3$

$$\begin{gathered} =\frac{4}{3}\times \mathrm{\pi }\times {\left(2\mathrm{r}\right)}^3 \\ =\frac{4}{3}\mathrm{\pi }\times 8{\mathrm{r}}^3 \\ =\frac{32}{3}{\mathrm{\pi r}}^3 \end{gathered}$$

Therefore, the correct option is (D).