A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is 39 and the height of the cylinder is 17 . If the volume of the solid is 150 pi, what is the area of the base of the cylinder?

1 Answer
Apr 7, 2017

The area of the base of the cylinder is 5pi.

Explanation:

The formula for volume of a cone is:
V=pir^2h/3

The formula for volume of a cylinder is:
V=pir^2h

Therefore the formula for the total volume (V_T) of the given solid is:

V_T=pir^2h_1/3+pir^2h_2 (where h_1=height of cone, and h_2=height of cylinder. The radius, r, is the same for both.)

V_T=pir^2(h_1/3+h_2)

We need to calculate r in order to calculate the area of the base of the cylinder, hence we fill in the data given.

150pi=pir^2(39/3+17)

We cancel the like term (pi) on each side.

150cancelpi=cancelpir^2(39/3+17)

150=r^2(13+17)

150=r^2xx30

Divide both sides by 30.

150/30=r^2

5=r^2

The formula of area of the base of a cylinder (a circle) is:

A=pir^2

A=pixx5

A=5pi