Question

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

$\mathrm{Volume}=4.5\mathrm{\pi }{\mathrm{cm}}^3$

Answer 1

Finding the radius of the sphere

We know that,

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

Given that, $\mathrm{Volume}=4.5\mathrm{\pi }{\mathrm{cm}}^3$

Therefore,

$$\begin{gathered} 4.5\mathrm{\pi }=\frac{4}{3}\mathrm{\pi }{\left(\mathrm{r}\right)}^3 \\ \frac{3}{4\mathrm{\pi }}*4.5\mathrm{\pi }={\mathrm{r}}^3 \\ 3.375={\mathrm{r}}^3 \end{gathered}$$

$$\begin{gathered} \sqrt[3]{3.375}=\sqrt[3]{\mathrm{r}3}(\mathrm{Taking}\mathrm{cube}\mathrm{on}\mathrm{both}\mathrm{sides}) \\ 1.5=\mathrm{r} \\ \mathrm{r}=1.5\mathrm{cm} \end{gathered}$$

Hence, radius of sphere is $1.5\mathrm{cm}$