Question

A bowl has a shape that can be generated by revolving the graph of y = x 2/2 between y = 0 and
y = 5 about the y-axis.
a. Find the volume of the bowl.
b. Related rates If we fill the bowl with water at a constant rate of 3 cubic units per second, how
fast will the water level in the bowl be rising when the water is 4 units deep?

Answer 1

volume of water in the bowl as a function of height ...

V = π ∫ ^h base 0 2ydy

take the derivative w/r to time

dV/dt= d/dt [π ∫^h base 0 2ydy]

If there is any confusion please leave a comment below.