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?

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?

anonymous · Answer

@luclucluc do you want to show your working?

anonymous · Answer

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

anonymous · Answer

You need to use the formula for Volume !

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Oh I see thank you so much !

anonymous · Answer

Don't overdo it :)