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A hemispherical tank with a radius of 9 m is filled from an inflow pipe at a rate of 2 m³/min (see figure). How fast is the water level rising when the water level is 8 m th² (3r-h) 3 from the bottom of the tank? (Hint: The volume of a cap of thickness h sliced from a sphere of radius ris 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. 1 V=97²-³² (Type an exact answer, using as needed.) Differentiate both sides of the equation with respect to t. dV dt (Type an exact answer, using as needed.) = 18th - th² dh dt When the water level is 8 m from the bottom of the tank, the water level is rising at a rate of about (Round to three decimal places as needed.) -.) Inflow 2 m/min 9 m

A hemispherical tank with a radius of 9 m is filled from an inflow pipe at a rate of 2 m³/min (see figure). How fast is the water level rising when the water level is 8 m th² (3r-h) 3 from the bottom of the tank? (Hint: The volume of a cap of thickness h sliced from a sphere of radius ris 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. 1 V=97²-³² (Type an exact answer, using as needed.) Differentiate both sides of the equation with respect to t. dV dt (Type an exact answer, using as needed.) = 18th - th² dh dt When the water level is 8 m from the bottom of the tank, the water level is rising at a rate of about (Round to three decimal places as needed.) -.) Inflow 2 m/min 9 m

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter65: Achievement Review—section Six
Section: Chapter Questions
Problem 44AR: Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places...
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A hemispherical tank with a radius of 9 m is filled from an inflow pipe at a rate of 2 m³/min (see figure). How fast is the water level rising when the water level is 8 m th² (3r-h) 3 from 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. 1 V=9h²-th²³ 3 (Type an exact answer, using as needed.) Differentiate both sides of the dh dt dV = ( 18th - th² equation with respect to t. dt (Type an exact answer, using as needed.) When the water level is 8 m from the bottom of the tank, the water level is rising at a rate of about (Round to three decimal places as needed.) -.-) Inflow 2 m³/min 9 m
Transcribed Image Text:A hemispherical tank with a radius of 9 m is filled from an inflow pipe at a rate of 2 m³/min (see figure). How fast is the water level rising when the water level is 8 m th² (3r-h) 3 from 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. 1 V=9h²-th²³ 3 (Type an exact answer, using as needed.) Differentiate both sides of the dh dt dV = ( 18th - th² equation with respect to t. dt (Type an exact answer, using as needed.) When the water level is 8 m from the bottom of the tank, the water level is rising at a rate of about (Round to three decimal places as needed.) -.-) Inflow 2 m³/min 9 m
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