Question

There are many cones with a volume of 72pi cubic inches. For example, one such cone could have a radius of 6 inches and a height of 6 inches.

Find another possible pair of measurements (radius and height) to make the same volume. (EXTRA CREDIT for each additional pair that you find.)

Answer 1

Explanation:

The volume of a cone of height h and circular base of radius r, is
`V = (\pi r^2 h)/(3)`. In this case we have that
`V=72\pi`.Then, we have that

`72\pi = (\pi r^2 h)/(3)`

multiplying by 3 on both sides and dividing by
`\pi` we have that

`216 = r^2\cdot h`

Suppose that we know the value of r, then we can find the value of h by solving h, that is

`h = (216)/(r^2)`.

So, by choosing any positive value of r, we can find the value for h. Note that if r=6, then
`h= (216)/(6^2) = 6`. This means that the amount of credit is infinite :)