Solution:
The formula for the volume of a cone is
[tex]V\text{ =}\frac{1}{3}h\pi r^2[/tex]where h is the height of the cone and r is the radius of the cone. This formula is equivalent to:
[tex]V\text{ =}\frac{h\pi r^2}{3}[/tex]now, by cross-multiplication, this is equivalent to:
[tex]3V=h\pi r^2[/tex]solving for the square of r, we get
[tex]r^2\text{ = }\frac{3V}{h\pi}[/tex]Applying the square root to both sides of the equation, we obtain:
[tex]r^{}\text{ = }\sqrt[]{\frac{3V}{h\pi}}[/tex]so that, the correct answer is:
[tex]r^{}\text{ = }\sqrt[]{\frac{3V}{h\pi}}[/tex]