
word problem calculus
An upright cylindrical tank with radius 7 m is being filled with water at a rate of 4 m3/min. How fast is the height of the water increasing? (Round the answer to four decimal places.)
A = pi * r^2 = 49 pi
(4 m^3 / min) / 49 pi m^2
= .2565 m / min
Can you plz help me with this and correct me because it may not be correct answer.
Thanks

You have the right answer but the setup looks very wrong to me.
You should start with $\displaystyle V=\pi r^2 h$ . r is constant so $\displaystyle V=49 \pi h$. Now take the derivative in terms of t. This leads to the same answer you got, but I don't know if you get the reason why it's this answer. Do you?

actually this is from online HW and the computer doesnt accept my answer.