Home > Student Resources > Solving Equations for Specific Variables

Solving Equations for Specific Variables

Solve the equation for the volume of a sphere for r (Radius)

$V=\frac{4}{3}\pi r^3$
We want r alone
$V=\frac{4}{3} r^3 \pi$
divide by $\frac{4}{3} \pi$
$\dfrac{3V}{4\pi}=r^3$
take the cube root of both sides
$\sqrt[3]{r^3}=\sqrt[3]{\dfrac{3V}{4\pi}}$
$r=\sqrt[3]{\dfrac{3V}{4\pi}}$