Cones

What is a Cone?

A cone is a special pyramid with a circular base that tapers to a point called the apex.

A cone may be right or skewed. A right circular cone is simply called a cone. In a right cone, the height is usually perpendicular to the base 

Volume of Cone = \( \frac{1}{3} \: \times \: \scriptsize area\:of\:base\:circle \: \times \: height \\ \frac{1}{3} \: \times \: \scriptsize \pi r^2 \: \times \: h \\ \frac{1}{3}\scriptsize \pi r^2 h\)

This formula shows that the volume of a cone is one-third the volume of a cylinder with the same radius and height as the cone. 

Example 6.1.1: 

The base diameter of a right cone is 16 cm, and the slant height is 10 cm. 

(a) Find the perpendicular height of the cone 
(b) Find the volume of the cone