#### JimmysJohnson

##### New member

- Joined
- Apr 18, 2020

- Messages
- 4

I was wondering if i could get some help on my understanding of this question.

"A cylinders radius is decreasing at the rate of 2cm/sec while it height is increasing at a rate of 3cm/sec. How fast is the cylinders volume changing when its radius is 10cm and its height 18cm?"

Since we know V = (pi)r

^{2}h

I thought that we could just use implicit differentiation to find the rate of change in respect to time. But in doing so i imagined that we'd simply use the product rule for the three terms (im not sure if this is where the flaw happens, but after a google search it seems as though it is possible).

After which we'll get

dV/dt = (r

^{2}h)+((pi)(2r)(dr/dt)(h))+((pi)(r

^{2})(dh/dt))

However when i sub in the respective points to solve for the rate of change of volume, i get very far off from the actual equation.

I understand that in order to solve the equation properly we take pi out of the equation

pi(r

^{2}h) and to go from there. I'm just not sure why my method doesn't work since its probably the methodology i'd instantly go for. Is it because pi is a constant and as such we can't differentiate it?

Thank you for your time and any/all help.