Question

The volume of a cone is 3rx? cubic units and its height is x units. Which expression represents the radius of the cone's base, in units?

O 3πx
O 6πx
O 3πx2
O 9πx2​

Answer 1

It is given that the volume of a cone =
`3\pi x^3` cubic units

Volume of cone with radius 'r' and height 'h' =
`(1)/(3)\pi r^2h`

Equating the given volumes, we get

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

`r^2h=3` ×
`3x^3`

`r^2h=9 x^3`

It is given that the height is 'x' units.

Therefore,
`r^2x=9x^3`

`r^2=9x^2`

Therefore,
`r=3 x`

So, the expression '
`3 x`' represents the radius of the cone's base in units.