An outdoor decorative pond in the shape of a hemispherical tank is to be lled with water
Question:
(a) The rate of change dV/dt of the volume of the water at time t is a net rate. Use this net rate to determine a differential equation for the height h of the water at time t. The volume of the water shown in the figure is V = ÏRh2 1/3 ph3,
where R = 10. Express the area of the surface of the water A = Ïr2 in terms of h.
(b) Solve the differential equation in part (a). Graph the solution.
(c) If there were no evaporation, how long would ittake the tank to fill?
(d) With evaporation, what is the depth of the water at the time found in part (c)? Will the tank ever be filled? Prove your assertion.
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Related Book For
A First Course in Differential Equations with Modeling Applications
ISBN: 978-1305965720
11th edition
Authors: Dennis G. Zill
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