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 `2750 pi`, what is the area of the base of the cylinder?

Answer 1

`110 pi` [square units]

Explanation:

`V_T=V_("cylinder")+V_("cone")`
`V_T=S_circ*h_("cylinder")+(S_circ*h_("cone"))/3`
`V_T=pi*r^2*h_("cylinder")+(pi*r^2*h_("cone"))/3`
`pi*r^2*(h_("cylinder")+h_("cone")/3)=V_T`

`pi*r^2=S_("cylinder's base")=(3*V_T)/(3*h_("cylinder")+h_("cone"))=(3*2750pi)/(3*14+33)=(8250pi)/75=110pi`[square units]