We can't find dh(oil)/dt directly. However, dh(oil)/dt is just dh(liquid)/dt - dh(water)/dt. Water also happens to form a conical shape, which means every single formula you derived in part (a) will also hold for (c).

When h(liquid) = 10, V(liquid) = 1000 pi, this means V(water) = 1000 pi / 3, and from there h(water) can be found, which allows us to find dV/dh(water).

dV(liquid)/dt = 6, so dV(water)/dt = 2.

tl;dr: Part (c) is just "redo part (a), but using h(water) instead of using h(liquid).