For the situation described in Exercise 32, what is the rate of change of the area of the exposed surface of the water when the water is 5 m deep?

Data from Exercise 32

A hemispherical tank with a radius of 10 m is filled from an inflow pipe at a rate of 3 m³/min (see figure). How fast is the water level rising when the water level is 5 m from the bottom of the tank? The volume of a cap of thickness h sliced from a sphere of radius r is πh² (3r - h)/3.

Transcribed Image Text:

Inflow 3 m/min 10 m