An equilateral triangle of side 14 centimeters is revolved about an altitude to form a cone. What is the number of cubic centimeters in the volume of the cone?

First find the height of the triangle using the Pythagorean theorem:

Height = √ (14^2 - 7^2)

Height = √ (196 - 49)

Height = √147

Height = 7 √3

Now find the volume of the cone:

Volume = PI x r^2 x H/3

Volume = 3.14 x 7^2 x 7√3/3

Volume = 621.8177 cubic cm's.

Round the answer as needed.