Turns out for this question we don't need to use formulas like volume of hemisphere, etc.

Instead, we are given an equation of a curve $x^2 + (y-5)^2 = 25$. We want the volume of the water in the bowl. Able to spot which topic can help us tackle that?

Integration applications! Notice that the bowl is formed when the curve $x^2 + (y-5)^2 = 25$ is rotated around the $y$-axis. Able to formulate the integral?

We have $\displaystyle \pi \int_0^h 25 - (y-5)^2 \; \mathrm{d}y$. Work out the integral and expand to get the show result.