A solid consists of a cone on top of a cylinder with a radius equal to the cone. The height of the cone is 6 and the height of the cylinder is 8. If the volume of the solid is 20π, what is the area of the base of cylinder?

1 Answer

πr2=SA=30π13

Explanation:

We have a Cone and a Cylinder. For ease of keeping track, I'm going to use N to indicate Cone and L to indicate Cylinder.

We know:

hN=6

hL=8

rL=rN and so I can refer to both as simply r

VN+VL=20π

What is the area of the base of the cylinder?

Let's first substitute in the formulas for the volumes of the two shapes:

VN=πr2h

VL=πr2h3

πr2hN+πr2hL3=20π and now substitute in values:

πr2(6)+πr2(8)3=20π

πr2(18)3+πr2(8)3=20π

πr2(26)3=20π

r2(26)3=20

r2(26)=60

r2=6026=3013

The area of the base is SA=πr2 and so:

πr2=SA=30π13