Question

A sphere has a volume of 2,304π mm3. Find the diameter of the sphere.

Answer 1

The volume of the sphere:

$V=2304\pi mm^3$

If r is the radius of the sphere is r, the volume formula can be expressed as:

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

Then:

$\begin{gathered} \frac{4}{3}\pi r^3=2304\pi \\ r^3=1728 \\ \Rightarrow r=12 \end{gathered}$

The diameter is two times the radius, then:

$\begin{gathered} D=2\cdot r \\ \therefore D=24mm \end{gathered}$