Another Cone problem!

May 2010
3
0
Sand is dropping on a pile that is shaped like a cone with the normal volume for a cone. The radius is growing at a rate of 2 cm per minute. The height is growing at a rate of 1cm per minute. How fast is the volume changing when the radius is 10 cm.

What do you take the derivative of? Before I was trying to take the derivative of the volume and having r be a function of t and h also a function of t... if you could show me the steps it would be a great help!

Thanks!

George
 

galactus

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Jul 2006
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Product rule:

\(\displaystyle \frac{dV}{dt}=\frac{\pi}{3}\left(r^{2}\cdot \frac{dh}{dt}+h\cdot 2r\frac{dr}{dt}\right)\)
 
May 2010
3
0
h???

I even got that far, but what do I substitute for h? h was not given, but only the change in h...

Thanks!
 
Dec 2009
3,120
1,342
I even got that far, but what do I substitute for h? h was not given, but only the change in h...

Thanks!
If the radius is growing at the rate of 2cm per minute,
then it will have taken x minutes to grow to 10cm.

Use that value of x to determine h, which grows at 1cm per minute.