Question

Find the radius of the sphere with a volume of $4500\mathrm{\pi }$$cubicyards$.

Answer 1

Finding the radius of the sphere when the volume is given

Let the radius of the sphere be $ryards$.

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

$$\begin{gathered} \therefore \frac{4}{3}{\mathrm{\pi r}}^3=4500\mathrm{\pi } \\ \Rightarrow \frac{4}{3}{\mathrm{r}}^3=4500 \end{gathered}$$ (Dividing both sides by $\mathrm{\pi }$)

$$\begin{gathered} \Rightarrow r^3=\frac{4500\times 3}{4} \\ \Rightarrow r^3=3375 \end{gathered}$$

$\Rightarrow \sqrt[3]{r^3}=\sqrt[3]{15\times 15\times 15}$ (Taking cube roots on both sides)

$\Rightarrow r=15yards$

Hence, the radius of sphere is $15yards$ .