Question

The volume of a cone is 3 X cubic units and its height is x units.

Answer 1

The  complete questions says:

The volume of a cone is $3\pi x^3$ cubic units and its height is x units.

Which expression represents the radius of the cone's base, in units?

Answer:

3x

Step-by-step explanation:

The volume of a cone is given by:

$V=\frac{1}{3}\pi r^2 h$

where

r is the radius of the base

h is the heigth of the cone

In this problem, we know:

The volume of the cone:

$V=3\pi x^3$ (1)

And its height:

$h=x$ (2)

We can re-arrange the formula above to make r, the radius, the subject:

$r=\sqrt{\frac{3V}{\pi h}}$

And by substituting (1) and (2), we find the radius:

$r=\sqrt{\frac{3(3\pi x^3)}{\pi x}}=\sqrt{9x^2}=3x$