A hemispherical tank with a radius of 7 m is filled from an inflow pipe at a rate of 2 m / min (see figure). How fast is the water level rising when the water level is 4 m from Inflow 2 m/min xh° (3r – h) the bottom of the tank? (Hint: The volume of a cap of thickness h sliced from a sphere of radius r is Let V be the volume of water in the tank and let h be the depth of the water. Write an equation that relates V and h. (Type an exact answer, using n as needed.)

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A hemispherical tank with a radius of 7 m is filled from an inflow pipe at a rate of 2 m / min (see figure). How fast is the water level rising when the water level is 4 m from
Inflow 2 m'/min
th (3r - h)
the bottom of the tank? (Hint: The volume of a cap of thickness h sliced from a sphere of radius r is
3
7 m
Let V be the volume of water in the tank and let h be the depth of the water. Write an equation that relates V and h.
(Type an exact answer, using t as needed.)
Transcribed Image Text:A hemispherical tank with a radius of 7 m is filled from an inflow pipe at a rate of 2 m / min (see figure). How fast is the water level rising when the water level is 4 m from Inflow 2 m'/min th (3r - h) the bottom of the tank? (Hint: The volume of a cap of thickness h sliced from a sphere of radius r is 3 7 m Let V be the volume of water in the tank and let h be the depth of the water. Write an equation that relates V and h. (Type an exact answer, using t as needed.)
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