Question

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.

Answer 1

The formula for the volume of a cone is

`V\text{ =}(1)/(3)h\pi r^2`

where h is the height of the cone and r is the radius of the cone. This formula is equivalent to:

`V\text{ =}(h\pi r^2)/(3)`

now, by cross-multiplication, this is equivalent to:

`3V=h\pi r^2`

solving for the square of r, we get

`r^2\text{ = }(3V)/(h\pi)`

Applying the square root to both sides of the equation, we obtain:

`r^{}\text{ = }\sqrt[]{(3V)/(h\pi)}`

so that, the correct answer is:

`r^{}\text{ = }\sqrt[]{(3V)/(h\pi)}`