Question

The volume of a cone is 3πx3 cubic units and its height is x units. Which expression represents the radius of the cone’s base, in units? 3x 6x 3πx2 9πx2

Answer 1

3x

Explanation:

Edge 2021

Answer 2

r=3x

Explanation:

The Volume of a Cone

The volume of a cone of radius r and height h is:

`\displaystyle V=(1)/(3)\pi hr^2`

We are given the volume of a cone is

`V=3\pi x^3`

Equating:

`\displaystyle (1)/(3)\pi hr^2=3\pi x^3`

Multiplying by 3:

`\pi hr^2=9\pi x^3`

Simplifying by pi:

`hr^2=9 x^3`

Since h=x:

`xr^2=9 x^3`

Dividing by x:

`r^2=9 x^2`

Taking square roots:

`r=√(9 x^2)=3x`

Thus: r=3x