Q:

If a cone has the same radius and height as a cylinder, the volume of the cone is one-fourth one-third half two-thirds the volume of the cylinder. If a cylinder and a sphere have the same radius and the cylinder’s height is twice its radius, then the volume of the sphere is one-fourth one-third half two-thirds the volume of the cylinder.

Accepted Solution

A:
The answer to this question would be:
First problem= one-third
Second problem= two-third

To answer this question, you need to know the formula for cylinder volume, cone volume and sphere volume. The formula would be:

cylinder volume = π * r^2 * h 
cone volume= π * r^2 * h /3
sphere volume= 4/3 π r^3

From the first problem, the radius and height of the cylinder are same as the cone. Then the calculation would be:
cone volume / cylinder volume= (π * r^2 * h /3) / (π * r^2 * h)= 1/3
The first answer is one-third.


For the second problem, the radius of the cylinder and sphere is same, but the cylinder height is twice as it radius. Then the calculation would be:

volume of sphere / volume of cylinder= (4/3 * π * r^3) / (π * r^2 * h)
(4/3 * π * r^3) / (π * r^2 * 2r) =
(4/3 * π * r^3) / (2 * π * r^3 ) =
(4/3)/2= 4/6 = 2/3
Then the second answer is two-third