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

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

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