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 24 24 and the height of the cylinder is 4 4. If the volume of the solid is 90 pi90π, what is the area of the base of the cylinder?

1 Answer
Dec 28, 2017

Base Area = 23.56=23.56

Explanation:

Combine the equations for the volumes of the cylinder and the cone to find the radius. Then calculate the base area (pir^2πr2).

V_"cone" = 1/3pir^2hVcone=13πr2h
V_"cyl" = pir^2hVcyl=πr2h

V = 90pi = 1/3pir^2h + pir^2hV=90π=13πr2h+πr2h

90 = 1/3r^2xx24 + r^2xx4 = 12r^290=13r2×24+r2×4=12r2
r^2 = 7.5r2=7.5

Because we want r^2r2 for the area anyway, we do not need to go further.
Base Area = pir^2 = pixx7.5 = 23.56πr2=π×7.5=23.56