An equilateral triangle is rotated about one its altitudes, sweeping out a cone in space. If the side length of the equilateral triangle is $12 \sqrt{3},$ then find the volume of the cone.

Please help, I really don't know what to do!

Guest Feb 27, 2020

#1**+1 **

The side length is 12√3 ...... 1/2 of this is the radius of the cone 6√3

The height of the cone = 6√3 * √3 = 6 * 3 = 18

So....the volume of this rotated equilateral triangle will be a cone with a radius of 6√3 and a height of 18

So .....the volume is

(1/3) pi * radius^2 * height =

(1/3) pi * (6√3)^2 ( 18) =

6 * 108 pi =

648 pi units^3

CPhill Feb 27, 2020