# Math Help - Finding height of cone

1. ## Finding height of cone

The radius of a traffic cone is 14 centimeters and the lateral surface of the cone is 1617 square centimeters. Find the height of the cone.

Don't know where to go from this.

2. Originally Posted by A Beautiful Mind
The radius of a traffic cone is 14 centimeters and the lateral surface of the cone is 1617 square centimeters. Find the height of the cone.

Don't know where to go from this.
Hi A Beautiful Mind,

The L.A. of a cone is given by $\pi r l$, where r = radius and l = slant height.

Therefore, $1617=\pi (14)l$

$l=\frac{1617}{14 \pi}$

Use the Pythagorean Theorem to find the height of the cone.

$\left(\frac{1617}{14 \pi}\right)^2=h^2+14^2$