Answer to Question #149992 in Geometry for yui

Question

PROBLEM 3. Find the radius of a cone of revolution of slant height 6 inches in which the total area is twice the lateral area.
FINAL ANSWER: _______________________________________

Answer 1

Slant Height is l= 6 inches. Let "r" be the radius of cone.

according the question, two times of lateral area of cone $S=\pi r l$ is equal to total area $A= \pi r l + \pi r^2$ .

$2S =A\\ \Rightarrow2\pi r l=\pi r l +\pi r^2\\ \Rightarrow l=r$

hence radius is equal to slant height which is 6 inches.