A cone has a slant height of 6 centimeters and a lateral area of 48(pi symbol) square centimeters. What is the volume of a sphere with a radius equal to that of the cone?

Answer 1

Lateral area = pi * r * sqrt( h^2 + r^2) = 48 *pi

4 * r* sqrt( h^2 + r^2) = 48

r* sqrt( h^2 + r^2) = 12

slant height = sqrt( h^2 + r^2) = 6

Then r * 6 = 12

r = 2

Volume = pi * r^2 * h

= pi * 2^2 * 6

= 24 * pi