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 `9` and the height of the cylinder is `6`. If the volume of the solid is `140 pi`, what is the area of the base of the cylinder?

Answer 1

Area of Base `= (140pi)/9`

Explanation:

Cone Volume = `(1/3)(pi)(r^2)h` where h = 9
Cylinder Volume = `(pi)(r^2)h` where h = 6

Note: Area of the Base = B= `(pi)(r^2)` so we can replace in the formulas as well since Radius is same for both solids.

Total Volume = Cone Volume + Cylinder Volume
`140pi = (1/3)B(9) + B(6)`
`140pi = 3B + 6B = 9B`
`B = (140pi)/9`