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 #66 # and the height of the cylinder is #5 #. If the volume of the solid is #64 pi#, what is the area of the base of the cylinder?
2 Answers
Explanation:
The volume of the cone is given by:
Since the height of the cone is 66, then
So,
The volume of a cylinder is given by:
Since the height of the cylinder is 5, then
So,
The total volume of the solid is
Therefore,
Since r is the radius, it must be have the restriction:
Therefore,
To find the base of the cylinder, we need to know that the base is a circle. The area of a circle is given by
The area of the base of the cylinder is:
Explanation:
The area of the base we need to find is:
The volume of the cylinder is:
where
The volume of the cone is
where
The volume of the solid is the sum of those two volumes:
Factoring
And that is the area of the base: