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 42 42 and the height of the cylinder is 1 1. If the volume of the solid is 480 pi480π, what is the area of the base of the cylinder?

1 Answer
Feb 20, 2017

The area of the base =32pi=100.5u^2=32π=100.5u2

Explanation:

Let a=a= area of the base

Volume of cone is V_(co)=1/3*a*h_(co)Vco=13ahco

Volume of cylinder is V_(cy)=a*h_(cy)Vcy=ahcy

Total volume

V=V_(co)+V_(cy)V=Vco+Vcy

V=1/3ah_(co)+ah_(cy)V=13ahco+ahcy

480pi=a(1/3*42+1)480π=a(1342+1)

480pi=a*15480π=a15

a=480/15pi=32pia=48015π=32π

a=100.5a=100.5