Question

A cone has a diameter of 3 inches. The cone holds 12 cubic inches of water, to the nearest inch.What is the height of the cone?

Answer 1

The formula of a volume of a cone:

$V=\dfrac{1}{3}\pi r^2H$

r - radius

H - height

We have a diameter d = 3in (d = 2r → r = d:2 → r = 3in : 2 = 1.5in)

and the volume 12in³.

Substitute:

$\dfrac{1}{3}\pi(1.5)^2H=12\qquad\text{multiply both sides by 3}\\\\2.25\pi H=36\qquad\text{divide both sides by 2.25}\pi\\\\H=\dfrac{36}{2.25\pi}\\\\H=\dfrac{16}{\pi}\ in\\\\H=\dfrac{16}{3.14}\to H\approx5\ in.$

Answer: The height is 5 in.