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 `66` and the height of the cylinder is `5`. If the volume of the solid is `324 pi`, what is the area of the base of the cylinder?

Answer 1

Area of the base of the cylinder is `12pi`

Explanation:

#{: (Vol_"cone",=1/3pir^2h_"cone",=22r^2pi), (ul(Vol_"cyl"),=pir^2h_"cyl",=ul(5r^2pi)), ("Total vol",,=27r^2pi) :}#

Since we are told the total volume is `324pi`
we have
`color(white)("XXX")27r^2pi=324pi`

`color(white)("XXX")rArr r^2=12`

#{: (Area_"base of cyl",=r^2pi,=12pi) :}#