Question

The height of a right cylinder is 3 times the radius of the base. The volume of the cylinder is 24 cubic units. What is the height of the cylinder?

Answer 1

`\large\boxed{H=\frac{6}{\sqrt[3]{\pi}}}`

Explanation:

The formula of a volume of a cylinder:

`V=\pi r^2H`

r - radius

H - height

We have V = 24 and H = 3r.

Substitute:

`24=\pi r^2(3r)\\\\24=3\pi r^3\qquad\text{divide both sides by}\ 3\pi\\\\(24)/(3\pi)=r^3\\\\r^3=(8)/(\pi)\to r=\sqrt[3]{(8)/(\pi)}\\\\r=\frac{\sqrt[3]{8}}{\sqrt[3]{\pi}}\\\\r=\frac{2}{\sqrt[3]{\pi}}\\\\H=3r\to H=3\cdot\frac{2}{\sqrt[3]{\pi}}\to H=\frac{6}{\sqrt[3]{\pi}}`