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 39 and the height of the cylinder is 17 . If the volume of the solid is 120 pi, what is the area of the base of the cylinder?

1 Answer
May 10, 2016

pir^2 = 40pi

Explanation:

This question is surprisingly simple, despite what look like awkward numbers.

"Vol cone" = 1/3pir^2h and "Vol cylinder" = pir^2H

Total volume = 1/3pir^2h + pir^2H = 120pi

1/3pir^2 39 + pir^2 17 = 120pirArr 1/cancel3pir^2cancel39^13 + pir^2 17 = 120pi

13pir^2 + 17 pir^2 = 120pi

30 pir^2 = 120pi" divide both sides by 30"

pir^2 = 40pi

Nothing more is needed, because the area of the circular base is given by pi r^2.