Question

A cylindrical tank with radius 5m is being filled with water at a rate of 3m^3/min. How fast is the height of the water increasing?


I got (3/25pi) -10h = dh/dt

but the answer is just 3/25pi

why?

Answer 1

@luclucluc do you want to show your working?

Answer 2

dv/dt= pi(2rh + dh/dtr^2)
isolate dh/dt=(dv/dt/pi)-2rh
then I subbed in dv/dt and r and got my answer

Answer 3

You need to use the formula for Volume !

Answer 4

isn't it v=(pi)r^2h? for a cylinder?

Answer 5

V = π r² h
At r = 5 -> V = 25π h
-> dV/ dt = 25π dh/ dt
=> dh/dt = 3 / (25π )

Answer 6

Oh I see thank you so much !

Answer 7

Don't overdo it :)