Cambridge Book Ch11 Extended Response Q4

[LinusX]

I tried doing the question and got stuck on even part ai 

I looked at the solutions book and they said I should integrate from -a to h-a for the total volume when
the depth is h. I don't understand why the upper terminal for the integration is h-a.
Do you guys have any idea what to do?

Cheers,
LinusX

P.S. Unfortunately I can't find my copy of the book CD so if anyone could upload the question it wold be great!

[Romperait]

Because the graph is defined for −a ≤ y ≤ 0 (i.e. the semicircle beneath the x axis), and height is relative from the bottom of the bowl, you can therefore find the volume enclosed at a certain height h by finding it between the bottom of the bowl at to where the height is defined which will be at .

Dunno if that really explained why it's but basically if you wanted to measure the height of a shape that goes from to , you'd find which ends up as .

[LinusX]

Oh lemme see if I understand. In this case, h is not the y value representing the top of the bowl, it is an actual distance
meaning that to find the y value, I have to add on the height onto the minimum y value.

Thank you so much Romperait!!!