Question

Find the height of a cone when its diameter is 8 inches and the volume is 100 cubic inches

Answer 1

`(75)/(4\pi )` inches or approximately 5.97 inches

Explanation:

Use the cone volume formula: V =
`\pi`r²
`(h)/(3)`

The diameter is 8 inches, so the radius will be 4 inches.

Plug in the radius and volume, and solve for h

V =
`\pi`r²
`(h)/(3)`

100 =
`\pi`(4²)(
`(h)/(3)`)

100 = 16
`\pi`
`(h)/(3)`

Divide each side by 16
`\pi`

`(25)/(4\pi )` =
`(h)/(3)`

Cross multiply and solve for h:

4
`\pi`h = 75

h =
`(75)/(4\pi )`

So, the cone's height is
`(75)/(4\pi )` or approximately 5.97 inches