Question

Which of the following functions gives the radius, r(v), of a conical artifact that is 20 inches tall as a function of its volume, v, in cubic inches?

Answer 1

By calculus or elementary geometry, we know that the formula for the volume of a cone, given pi (the constant), its height h and its radius r is:

`V=pi*h*r^2/3`
Lets solve this relation for the radius:

`3V=pi*h*r^2`

`(3V)/(pi*h) =r^2`

`\sqrt{(3V)/(pi*h)} = r`
Now we have found a general formula that gives us the radius of a cone, given its volume and height. We need only substitute height (20in) and pi=3.14 to get the numerical equation: r=0.2185*
`√(V)`