Question

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 `33` and the height of the cylinder is `14`. If the volume of the solid is `75 pi`, what is the area of the base of the cylinder?

Answer 1

I got `9`

Explanation:

Consider the diagram:

Where:
`h1=33`
`h2=14`

The volume will be:
`V=`volume of cylinder+volume of cone`=75pi`
or:
`pir^2*h2+1/3pir^2h1=75pi`
solving for `r`:
`cancel(pi)r^2*h2+1/3cancel(pi)r^2h1=75cancel(pi)`
`r^2(14+33/3)=75`
`r^2=75/(14+11)=3`
So
base area`=pir^2=3.14*3=9.42~~9`