# Rate of change question (pretty confusing)

3. The volume of a tank used to provide water for animals at an animal enclosure at the local show is given by V(h) = (0.2h^3+3h)m^3 where h metres is the depth of the water in the tank at any time t seconds. Water is being added to the tank at a constant rate of 0.4 m3 per second. Find the rate at which the water level is rising when the depth of water in the tank is 2.1 metres.

So i differentiated the equation: v(h) = (0.2h^3+3h) m^3, which is v'(h) = (0.6h^2+3) m^3. But because the limit is 2.1m, and the amount of liquid going into the object is going in at 0.4m^3 a second. so if i use v'(2.1)= (0.6h^2+3) m^3 and solve for h.. i can divide h by 0.4 and find out the time it took to reach 2.1m?

Thank you.

## Answers and Replies

U need to find dH/dt, i.e the rate at which water level is rising,,
lets say, dV/dH=(dV/dt).(dt/dH).
write dV/dH expression, from the relation given at h=2.1 m.
since know what dV/dt is i.e, o.4 m^3/sec, u can find out dH/dt!!!!!!!

What was the answer you got? I got 0.071 m/s.

i got 0.053

Mentallic
Homework Helper
Then I'll confirm that Anakin_k is correct.

I think it should be dV/dT = dH/dT * dV/dH rather than what you had, Mandeep.

its all the same!!! u cn write it whichever way u wish too
u have dV/dt, dV/dh... its not a big deal to get dH/dt

dude m really sorry..... i messd up the calc..
its 0.071 only!!!!

dude m really sorry..... i messd up the calc..
its 0.071 only!!!!

A piece of writing advice. You don't really need to put exclamation marks in everything you write. At some point it starts to lose its meaning. In fact, in a math homework forum I dare say an exclamation point would probably never be necessary.

Mentallic
Homework Helper
In fact, in a math homework forum I dare say an exclamation point would probably never be necessary.

But if I couldn't use exclamation marks then what good does does it this equality? 3+3=3!

I think you must be really excited about 3+3=3. I, on the other hand, know that 3+3!=3. :p

Mentallic
Homework Helper
I think you must be really excited about 3+3=3.
I never claimed this. Please, quote specifically where I ever claimed such an invalid response in any of my posts here.

I, on the other hand, know that 3+3!=3. :p
You don't know very much then do you :tongue:

Mark44
Mentor
But if I couldn't use exclamation marks then what good does does it this equality? 3+3=3!

I think you must be really excited about 3+3=3. I, on the other hand, know that 3+3!=3. :p

A few spaces would make it more clear that you meant 3 + 3 != 3, or better yet, 3 + 3 $\neq$ 3.