A hemispherical tank with a radius of 8 m is filled from an inflow pipe at a rate of 3 m/ min (see figure). How fast is the water level rising when the water level is 5 m from the bottom f the tank? Inflow 3 m /min xh° (3r = h) (Hint: The volume of a cap of thickness h sliced from a sphere of radius r is 3 8 m Let V be the volume water in the tank and let h be the depth of the water. Write an equation that relates V and h. ah? (24 – h) 3 %3D (Type an exact answer, using x as needed.) Differentiate both sides of the equation with respect to t. - ( 16th – xh² ) dv dh dt (Type an exact answer, using x as needed.) When the water level is 5 m from the bottom of the tank, the water level is rising at a rate of about (Round to three decimal places as needed.)
A hemispherical tank with a radius of 8 m is filled from an inflow pipe at a rate of 3 m/ min (see figure). How fast is the water level rising when the water level is 5 m from the bottom f the tank? Inflow 3 m /min xh° (3r = h) (Hint: The volume of a cap of thickness h sliced from a sphere of radius r is 3 8 m Let V be the volume water in the tank and let h be the depth of the water. Write an equation that relates V and h. ah? (24 – h) 3 %3D (Type an exact answer, using x as needed.) Differentiate both sides of the equation with respect to t. - ( 16th – xh² ) dv dh dt (Type an exact answer, using x as needed.) When the water level is 5 m from the bottom of the tank, the water level is rising at a rate of about (Round to three decimal places as needed.)
Calculus: Early Transcendentals
8th Edition
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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Transcribed Image Text:A hemispherical tank with a radius of 8 m is filled from an inflow pipe at a rate of 3 m° / min (see figure). How fast is the water level rising when the water level is 5 m from the bottom of the tank?
Inflow 3 m³ /min
ah? (3r - h)
2
(Hint: The volume of a cap of thickness h sliced from a sphere of radiusr is
3
8 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.
th? (24 – h)
V =
(Type an exact answer, using t as needed.)
Differentiate both sides of the equation with respect to t.
dV
dh
16th – Th )
dt
dt
(Type an exact answer, using a as needed.)
When the water level is 5 m from the bottom of the tank, the water level is rising at a rate of about
(Round to three decimal places as needed.)
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