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 36 and the height of the cylinder is 8. If the volume of the solid is 64π, what is the area of the base of the cylinder?

1 Answer
Nov 16, 2016

20.1

Explanation:

A Conical Volume is given by:
V=13πr2h
A Cylindrical Volume is given by:
V=πr2h
Circular Area (base of cylinder)
A=2πr2

Total solid volume =
64π=13πr2h1+πr2h2

Solve for r.
64=13r236+r28 ; 64=r212+r28
64=r220 ; 6420=r2 ;

r2 = 3.2 ; r = 1.79

A=2π3.2=20.1