Question

Find the volume of a cone with a base area 36pi and a height equal to twice the radius

Answer 1

The volume of a cone is $V= \frac{1}{3} A_{\text{basis}}\cdot H$. Since $A_{\text{basis}}=36\pi$ and you know that basis is a circle you can conclude that $\pi R^2=36\pi$ and $R=6$.

If height $H$ equal to twice the radius $R$, then $H=2R=2\cdot 6=12$.

The volume will be:$V= \frac{1}{3} \cdot 36\pi \12=144\pi$ cubic units.