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

• Dec 9th 2012, 12:01 PM
roharia
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 700ft3 of grain?

Height of the pile =?
• Dec 9th 2012, 12:33 PM
skeeter
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 700ft3 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.