Question

Find the radius of the sphere with the given volume. Round your answer to the nearest tenth if necessary.

$\mathrm{Volume}=180{\mathrm{ft}}^3$

Answer 1

We know that, volume of sphere given by:

$V=\frac{4}{3}{\mathrm{\pi r}}^3$

$$\begin{gathered} 180=\frac{4}{3}\mathrm{\pi }{\left(\mathrm{r}\right)}^3\mathrm{Substittue} \\ \frac{3}{4\mathrm{\pi }}*180={\mathrm{r}}^3 \\ 42.97={\mathrm{r}}^3 \end{gathered}$$

$$\begin{gathered} \sqrt[3]{42.97}=\sqrt[3]{\mathrm{r}3}(\mathrm{Taking}\mathrm{cube}\mathrm{on}\mathrm{both}\mathrm{sides}) \\ 3.50=\mathrm{r} \end{gathered}$$

Hence, the radius of sphere is about $3.5ft$.