volume of right circular cone

Question

Find the volume of right circular cone with a base radius of 8 cm and a slant angle of 32.

Answer 1

Here is a sketch;

Using trigonometry, we can calculate the height (h) from the right triangle formed in the middle of the cone using:

tan(32°) = h/8

h = 8tan(32°)

Plugging this in a calculator, we get h = 4.999

The volume of a cone is then easily calculated from V = 1/3πr²h = 1/3(π)(8²)(4.999)

I'll let you do the rest