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!
+130536 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
