What is the height of a cone with a radius of 12 cm and a volume of 408*pi cubic cm.

All we have to do is to recall the identity that gives the
volume of a cone:

V =
pi*R^2*h/3

R is the radius of the base circle and h is the
height of the cone.

Since we know the values of the volume
and the radius, we'll replace them into the formula:

408*pi
= pi*144*h/3

We'll divide by
pi:

408*3 = 144*h

We'll divide
by 144 both sides:

h =
408*3/144

h = 1224/144

h = 8.5
cm

The requested height of the cone is of 8.5
cm.