Question

what is the radius of a sphere with a volume of 36,000 Pi mm3?

Answer 1

The volume of a Sphere was determined using the following formula:

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

Given that you know the volume of the sphere, you can determine its radius.

First, let's write the formula for r:

- multiply both sides of the equal sign by the reciprocal fraction of 4/3π to leave the r term alone on the left side of the formula:

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

-apply the cubic root to both sides of the equal sign

$\begin{gathered} \sqrt[3]{V\cdot\frac{3}{4}\pi}=\sqrt[3]{r^3} \\ \sqrt[3]{V\cdot\frac{3}{4}\pi}=r \end{gathered}$

Replace the expression obtained with the given volume of the sphere:

$\begin{gathered} r=\sqrt[3]{36000\pi\cdot\frac{3}{4}\pi} \\ r=\sqrt[3]{27000} \\ r=30 \end{gathered}$

The radius of the sphere is 30mm long