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

Answer:

Step-by-step explanation:

The volume of a cone of height h and circular base of radius r, is $V = \frac{\pi r^2 h}{3}$. In this case we have that $V=72\pi$.Then, we have that

$72\pi = \frac{\pi r^2 h}{3}$

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

$h = \frac{216}{r^2}$.

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