Answer:
r=3x
Step-by-step explanation:
The Volume of a Cone
The volume of a cone of radius r and height h is:
[tex]\displaystyle V=\frac{1}{3}\pi hr^2[/tex]
We are given the volume of a cone is
[tex]V=3\pi x^3[/tex]
Equating:
[tex]\displaystyle \frac{1}{3}\pi hr^2=3\pi x^3[/tex]
Multiplying by 3:
[tex]\pi hr^2=9\pi x^3[/tex]
Simplifying by pi:
[tex]hr^2=9 x^3[/tex]
Since h=x:
[tex]xr^2=9 x^3[/tex]
Dividing by x:
[tex]r^2=9 x^2[/tex]
Taking square roots:
[tex]r=\sqrt{9 x^2}=3x[/tex]
Thus: r=3x
