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

Answer:

3x

Step-by-step explanation:

Edge 2021

Answer 2

Answer:

r=3x

Step-by-step explanation:

The Volume of a Cone

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

$\displaystyle V=\frac{1}{3}\pi hr^2$

We are given the volume of a cone is

$V=3\pi x^3$

Equating:

$\displaystyle \frac{1}{3}\pi hr^2=3\pi x^3$

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:

$r=\sqrt{9 x^2}=3x$

Thus: r=3x