An equilateral triangle of side 12 centimeters is rotated about an altitude to form a cone. What is the number of cubic centimeters in the volume of the cone?

michaelcai
Oct 24, 2017

#1**+1 **

volume of cone = (1/3)(pi)(radius)^{2}(height)

The height of the cone will be the same as the height of the triangle.

height = 12 sin 60° = 12 √3 / 2 = 6√3

The radius of the cone will be half of the base of the triangle.

radius = 12 / 2 = 6

So.. volume of cone = (1/3)(pi)(6)^{2}(6√3) = (1/3)(pi)(36)(6√3) = 72 pi √3 cubic centimeters

hectictar
Oct 24, 2017

#1**+1 **

Best Answer

volume of cone = (1/3)(pi)(radius)^{2}(height)

The height of the cone will be the same as the height of the triangle.

height = 12 sin 60° = 12 √3 / 2 = 6√3

The radius of the cone will be half of the base of the triangle.

radius = 12 / 2 = 6

So.. volume of cone = (1/3)(pi)(6)^{2}(6√3) = (1/3)(pi)(36)(6√3) = 72 pi √3 cubic centimeters

hectictar
Oct 24, 2017