A bowl contains water that evaporates at a rate proportional to the surface area of water exposed to the air (Figure 19). Let A(h) be the cross-sectional area of the bowl at height h.
(a) Explain why V(h + Δh) − V(h) ≈ A(h)Δh if Δh is small.
(b) Use (a) to argue that dV/dh = A(h).

(c) Show that the water level h decreases at a constant rate.

Transcribed Image Text:

H ΔΗ h V(h+Ah) - V(h) - V(h) = volume up to height h Cross-sectional area A (h)