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.

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- Sep 8th 2009, 11:20 AMA Beautiful MindFinding 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. - Sep 8th 2009, 11:52 AMmasters
Hi A Beautiful Mind,

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

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

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

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

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