### Home > CALC > Chapter 1 > Lesson 1.4.2 > Problem1-159

1-159.

The height of a right circular cone is twice the radius. If the height of the cone is $h$, find the volume of the cone using only $h$.

The volume of a cone is $\frac{1}{3}Bh$, where $B=\pi r^{2}$.
Since $h$ is twice the radius, how can you write $r$ in terms of $h$?

$V=\frac{1}{3}\pi r^2h=\frac{1}{3}\pi\Big(\frac{1}{2}h\Big)^2=\frac{\pi h^3}{12}$