The complete questions says:
The volume of a cone is [tex]3\pi x^3[/tex] 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:
[tex]V=\frac{1}{3}\pi r^2 h[/tex]
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:
[tex]V=3\pi x^3[/tex] (1)
And its height:
[tex]h=x[/tex] (2)
We can re-arrange the formula above to make r, the radius, the subject:
[tex]r=\sqrt{\frac{3V}{\pi h}}[/tex]
And by substituting (1) and (2), we find the radius:
[tex]r=\sqrt{\frac{3(3\pi x^3)}{\pi x}}=\sqrt{9x^2}=3x[/tex]
