Question

The volume of a cylinder is 40ft^3. Which expression represents the volume of a cone with the same base and height as the cylinder?

3(40)ft^3
3(1/40)ft^3
1/3(40)ft^3
1/3(40^2)ft^3

Answer 1

The third one, 1/3(40)ft^3, due to the fact that the volume of a cone is 1/3 that of a cylinder. This is shown from their formulas.
Cylinder

`\pi r^(2) h`
Cone

`( \pi r^(2) h)/(3)`

Answer 2

The volume of a cone is
`(1)/(3)(40)\ ft^(3)` .

Explanation:

Formula

`Volume\ of\ a\ cylinder = \pi r^(2) h`

`Volume\ of\ a\ cone = (1)/(3) \pi r^(2) h`

Where r is the radius and h is the height .

As given

The volume of a cylinder is 40 ft ³ .

`40= \pi r^(2) h`

`Volume\ of\ a\ cone = (1)/(3)* 40`

`Volume\ of\ a\ cone = (1)/(3)(40)\ ft^(3)`

Therefore the volume of a cone is
`(1)/(3)(40)\ ft^(3)` .