Question

A cylinder has a height of 11 meters and a volume of approximately 1243 cubic feet. What is the height of a cone with the same volume and radius as the cylinder?

Answer 1

Explanation:

Comment

There is a short cut to this and we might just as well use it. Start by writing the general formulas for the volume of a cylinder and the volume of the cone

Equation

V_cylinder = pi * r^2 * h

V_Cone = (1/3) pi * r^2 * h1

Solution

The volumes are equal, so the right sides must be equal as well

pi * r^2 * h = (1/3)*pi * r^2 * h1 Divide both sides by pi

r^2 * h = (1/3) * r^2 * h1 Divide both sides by r^2

h = (1/3) * h1 Multiply both sides by 3

3*h = h1 h = 11 (given)

3*11 = h1

33 = h1

Answer: the cone's height = 33 meters.