JimmysJohnson
New member
- Joined
- Apr 18, 2020
- Messages
- 4
G'day again.
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)r2h
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 = (r2h)+((pi)(2r)(dr/dt)(h))+((pi)(r2)(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(r2h) 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.
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)r2h
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 = (r2h)+((pi)(2r)(dr/dt)(h))+((pi)(r2)(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(r2h) 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.