Question

A sphere and a cylinder each have the same radius. The cylinder has a height that is triple the radius. How do I create a simplified expression to show how many times greater the larger figure is than the other figure?

Answer 1

we are given a sphere and a cylinder with the following conditions:

`r_s=r_c=r`
`h=3r`

The volume of the sphere is given by the following formula:

`V_s=(4)/(3)\pi r^3`

The volume of the cylinder is given by:

`V_c=\pi r^2h`

Since the height "h" is three times the radius "r", we get_

`V_c=3\pi r^3`

Now we divide both sides by 3:

`(V_c)/(3)=\pi r^3`

Now we replace the right sides of the volume of the sphere for its equivalent in the volume of the cylinder:

`V_s=(4)/(3)((V_c)/(3))`

Solving:

`V_s=(4)/(9)V_c`

Multiplying by 9/4:

`(9)/(4)V_s=V_c`

Therefore, the cylinder occupies 9/4 of the volume of the sphere.