Question

1. The formula for the volume of a cone is

V =
2h.
where r is the radius of the base and h is the height of the cone.
Part A: Solve the formula for r.

Answer 1

3 v 3.14/h

Explanation:

equation

Answer 2

`r=\sqrt{(3V)/(\pi\ h)}`

Explanation:

The volume of cone is given by:

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

where
`r` is the radius of the base and
`h` is the height of the cone.

We need to solve for
`r`

we have
`V=(1)/(3)\ \pi\ r^2\ h`

Multiplying both sides by 3 to remove
`(1)/(3)`

⇒
`3* V=3* (1)/(3)\ \pi\ r^2\ h`

⇒
`3V=\pi\ r^2\ h`

dividing both sides by
`\pi\ h`

⇒
`(3V)/(\pi\ h)=(\pi r^2 h)/(\pi\ h)`

⇒
`(3V)/(\pi\ h)=r^2`

Taking square root both sides:

⇒
`\sqrt{(3V)/(\pi\ h)}=√(r^2)`

⇒
`\sqrt{(3V)/(\pi\ h)}=r`

∴
`r=\sqrt{(3V)/(\pi\ h)}`