Question

The volume of a cylinder is 4 pi x3 cubic units and its height is x units.

Which expression represents the radius of the cylinder, in units?
2x
4x 2 pi x2 4 pi x2

Answer 1

`2x`

Explanation:

The volume of a cylinder,
`V` is given by the formula,

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

Where,
`r` is the radius and
`h` is the height of the cylinder.

Here,
`V=4\pi x^(3)`,
`h=x`. Plug in these values and solve for radius,
`r`.

This gives,

`V=\pi r^(2)h\\4\pi x^(3)=\pi r^(2)x\\r^(2)=(4\pi x^(3))/(\pi x)\\r^(2)=4x^(2)\\`

Taking square root both sides, we get

`\sqrt{r^(2)}=\sqrt{4x^(2)}\\r=2x`

Therefore, the radius of the cylinder can be expressed as
`2x`.