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 and the height of the cylinder is 6 . If the volume of the solid is 45 pi, what is the area of the base of the cylinder?

1 Answer
Mar 19, 2018

2.25pi units squared

Explanation:

To find the area, we first need to find the radius. We know that the total volume of the cylinder plus the cone is 45pi, which is found by adding the volumes of the cylinder (6r^2pi) and the cone ((42r^2pi)/3), where r represents the unknown radius of the cone's and cylinder's bases.

Cylinder's volume: pir^2*h

Cone's volume: (pir^2*h)/3

Add the two volumes together:

6r^2pi+(42r^2pi)/3=45pi

(18r^2pi)/3 +(42r^2pi)/3=45pi

(60r^2pi)/3=45pi

60r^2pi=135pi

60r^2=135

r^2=2.25

r=+-1.5 rarr Disregard the -1.5, a length cannot be negative

Area is pir^2

pi*1.5^2

pi*2.25

The answer is 2.25pi