The formula for the volume of a cone is V = {ærh, where r is the radius of thecone and h is the height of the cone. Rewrite the formula to solve for the positivevalue of r in terms of h and V.

Respuesta :

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]