Question

Using your algebra skills, how can you rearrange the formula for the volume of a cone, , to find an expression for radius r when you're given h and V? Remember to perform the same operations on both sides of the equation.

Answer 1

Volume of a cone:

$V = \dfrac{\pi r^{2} h}{3}$

//Multiply 3 on both sides:

$3v = \pi r^{2} h$

//Divide πh on both sides:

$\dfrac{3v}{\pi h} = r^{2}$

//Square root both sides:

$\sqrt{\dfrac{3v}{\pi h}} = r$

//Rewrite with r as the subject:

$r = \sqrt{\dfrac{3v}{\pi h}}$