Need to find the height of something based on certain information.

I know the answer to the problem (5.508), but I'm not sure how to do it myself for a test or something. If someone could do it out so I can learn how to do it, because I have bout 6 more of these to do on my own. Thank you.

Grain is falling from a chute onto the ground, forming a conical pile whose diameter is always 4 times its height. How high is the pile to the nearest hundredth of a foot when it contains 700*f**t*3 of grain?

Height of the pile =?

Re: Need to find the height of something based on certain information.

Quote:

Grain is falling from a chute onto the ground, forming a conical pile whose diameter is always 4 times its height. How high is the pile to the nearest hundredth of a foot when it contains 700ft^{3} of grain?

Height of the pile =?

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

you are given $\displaystyle d = 4h \implies 2r = 4h \implies r = 2h$

substitute $\displaystyle 2h$ for $\displaystyle r$ and 700 for $\displaystyle V$ in the volume equation, then solve for $\displaystyle h$

btw ... this is not a calculus problem.