Question

What is the diameter of a sphere with a volume of 72 in”, to thenearest tenth of an inch?

Answer 1

The volume of a sphere can be calculated with the following equation:

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

Where V is the volume and r is the radius.

We can manipulate the equation and solve for:

$r^3=\frac{3}{4\pi}V$$r^{}=\sqrt[3]{\frac{3}{4\pi}V}$$\begin{gathered} r^{}=\sqrt[3]{\frac{3}{4\pi}72in^3} \\ r\approx2.580762in \end{gathered}$

The diameter is twice the radius (2*2.580762in), giving 5.1615in, rounded to 5.2in