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 9 and the height of the cylinder is 12 . If the volume of the solid is 15 pi, what is the area of the base of the cylinder?

1 Answer
Fleur
Aug 16, 2017

pi

Explanation:

The base of a cylinder is a circle. The area of a circle is pir^2; however, we do not know the radius. To find r, we can use the information given in the problem.

The volume of a cone is 1/3pir^2h, where r is the radius and h is the height. We know the height is 9, so we can say

V_"cone" = 1/3pir^2*9 = 3pir^2

The volume of a cylinder is pir^2h, and we know the height is 12.

V_"cylinder" = pir^2*12 = 12pir^2

We also know that the volume of the cone plus that of the cylinder is equal to 15pi.

V_"cone" + V_"cylinder" = 15pi

3pir^2 + 12pir^2 = 15pi

15pir^2 = 15pi

Dividing by 15pi on both sides, we get

r^2 = 1

r=1

So, the area of the base of the cylinder is

pir^2 = pi* 1^2 = pi

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