The inner surface of a bowl is the shape formed by rotating completely about the y-axis the area bound by the curve y=${x^2}$—2, the x-axis, the y-axis and the line y=3.
(i) find the volume of the bowl (I’ve already solved this one)
(ii) determine the formula that represents the volume of water in the bowl when the depth of water is d(<3) (this is the part I’m having trouble with)
Question (ii) isn’t worth many points so I’m assuming there shouldn’t be much to it. I considered subtracting the volume of the part without water from the total volume but this feels incorrect since I’d need to find a formula for this volume too.
Then I need to find the rate at which the depth is increasing when d=1 if water is poured in at a rate of 5 cubic units per second. I feel that I can figure this one out fairly easily once I know the answer to (ii).
I’d really be grateful for any help/hints. Thank you