solve for radius of a cone with given volume

Question

a cone has a volume of 288pi. the height of the cone if half the radius of the base of the cone, what's the radius? What is th fastest way to solve this?

A. 6

B. 9

C. 12

D. 15

Answer 1

V=(1/3)∏r^2h

288∏=(1/3)∏r^2(r/2)

288∏=∏(r^3/6)

divide both sides by pi

288=r^3/6

288*6=r^3

1728=r^3

1728=2*2*2*2*2*2*3*3*3=(2*2*3)*(2*2*3)*(2*2*3)=12*12*12

r=12 which is C.