Question

If a cylinder has a volume of 75 cubic inches, what would be the volume of a cone with the same base and hieght?

Answer 1

25 cubic inches.

Step-by-step explanation:

The volume of a cylinder is calculated as:

`V_{\text{Cylinder}}=B^{}\cdot h`

Where B is the area of the base and h is the height of the cylinder.

Additionally, the volume of the cone can be calculated as:

`V_{\text{cone}}=(1)/(3)(B\cdot h)`

Where B is the area of the base and h is the height of the cone.

So, if the cylinder and cone have the same base and height, we can relate both volumes as:

`V_{\text{cone}}=(1)/(3)(V_{\text{cylinder}})`

Because we replace (B·h) with Vcylinder.

Now, if the cylinder has a volume of 75 cubic inches, the volume of the cone is:

`\begin{gathered} V_{\text{cone}}=(1)/(3)(75) \\ V_(cone)=25 \end{gathered}`

Therefore, the answer is 25 cubic inches.