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

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The volume of a cone is given by (1/3)*pi*r^2*h, where r is the radius and h is the height.

The volume is 408*pi and the radius is 12

408*pi = (1/3)*pi*12^2*h

=> 408*pi = 48*pi*h

=> h = 408*pi/(48*pi)

=> h = 8.5

**The height of the cone is 8.5 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.**