Question

The volume of a right circular cone is 300 cubic inches. What is the volume, in cubic inches, of a right cylinder th

has the same base and height as the cone?

Answer 1

The volume of the cylinder is 900 cubic inches

Explanation:

Given

Let V1 represent the volume of a cone and V2 represents the volume of a cylinder

`V_1 = 300in^3`

Required

Determine the volume of a cylinder with same dimension

The volume of a cone is calculated as:

`V_1 = (1)/(3)\pi r^2h`

The volume of a cylinder is calculated as:

`V_2 = \pi r^2h`

Since, the cone and cylinder have the same dimensions, we can substitute
`\pi r^2h` for
`V_2` in
`V_1 = (1)/(3)\pi r^2h`

So, we have:

`V_1 = (1)/(3) * V_2`

Multiply both sides by 3

`3 * V_1 = (1)/(3) * V_2 * 3`

`3 * V_1 = V_2`

`V_2 = 3 * V_1`

Substitute
`300in^3` for
`V_1`

`V_2 = 3 * 300in^3`

`V_2 = 900in^3`

Hence, the volume of the cylinder is 900 cubic inches