A hemispherical tank with a radius of 8 m is filled from an inflow pipe at a rate of 4 m^3/min (see figure). How fast is the water level rising when the water level is 6 m from the bottom of the tank? (Hint: The volume of a cap of thickness h sliced from a sphere of radius r is πh^2(3r−h)/3.)

A hemispherical tank with a radius of 8 m is filled from an inflow pipe at a rate of 4 m^3/min (see figure). How fast is the water level rising when the water level is 6 m from the bottom of the tank? (Hint: The volume of a cap of thickness h sliced from a sphere of radius r is πh^2(3r−h)/3.)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section: Chapter Questions

Problem 47RE

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Question

A hemispherical tank with a radius of 8 m is filled from an inflow pipe at a rate of 4 m^3/min (see figure).

How fast is the water level rising when the water level is 6 m from the bottom of the tank?

(Hint: The volume of a cap of thickness h sliced from a sphere of radius r is πh^2(3r−h)/3.)

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