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 27 and the height of the cylinder is 11 . If the volume of the solid is 190 pi, what is the area of the base of the cylinder?

1 Answer
Jun 22, 2016

Area of base = pir^2 = 9.5pi

Explanation:

Start by writing down the formulae for the volumes of the two shapes: They have the same radius, but different heights.
Cone: V = 1/3 pi r^2h" Cylinder: "V = pi r^2H

V = 1/3 pi r^2h + pi r^2H = 190pi

Factorise: pi r^2(1/3 h + H) = 190pi

Substitute: pi r^2(1/3xx 27 + 11) = 190pi

pi r^2(9+11) = 190pi

20pir^2 = 190pi

The area of the base of the cylinder is pir^2, so solve for this

pir^2 = (190pi)/20

Area of base = pir^2 = 9.5pi