CPM Homework Help : CALC3RD Problem 1-159

The height of a right circular cone is twice the radius. If the height of the cone is $h$ , write an expression for the volume of the cone using only $h$ .

Hint:

$\text{The volume of a cone is }\frac{1}{3}Bh, \text{ where }B=\pi r^{2}.$

Since $h$ is twice the radius, how can you write $r$ in terms of $h$ ?

Answer:

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