The radius of a right circular cylinder is increasing at the rate of 3 ft/sec, while the height is decreasing at the rate of 6 ft/sec. At what rate is the volume of the cylinder changing when the radius is 15 ft and the height is 10 ft?

Question

tkhunny · Answer

Formula for the volume fo a right circular cylinder, please...

anonymous · Answer

$$v=pir^2h$$

anonymous · Answer

$$v=\pi r^2h$$

tkhunny · Answer

That's good.  Now, rewrite with everything as a function of time.

$v(t) = \pi \left(r(t)\right)^{2}h(t)$

You don't HAVE to do that.  You can just think it.

Find the complete derivative, $\dfrac{dv}{dt}$.  This is the calculus part.  The rest is algebra.

dumbcow · Answer

$$\frac{dV}{dt} = \frac{dV}{dr}*\frac{dr}{dt} +  \frac{dV}{dh}*\frac{dh}{dt}$$
$$ = (2 \pi r h)\frac{dr}{dt} + (\pi r^2) \frac{dh}{dt}$$
Sub in all the given conditions for r,h, dr/dt , dh/dt

tkhunny · Answer

I guess we'll never know if the OP can do it.