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A draining hemispherical reservoir Water is flowing at the
Chapter 3, Problem 29E(choose chapter or problem)
Problem 29E
A draining hemispherical reservoir Water is flowing at the rate of from a reservoir shaped like a hemispherical bowl of radius 13 m, shown here in profile. Answer the following questions, given that the volume of water in a hemispherical bowl of radius R is when the water is y meters deep.
a. At what rate is the water level changing when the water is 8 m deep?
b. What is the radius r of the water’s surface when the water is y m deep?
c. At what rate is the radius r changing when the water is 8 m deep?
Questions & Answers
QUESTION:
Problem 29E
A draining hemispherical reservoir Water is flowing at the rate of from a reservoir shaped like a hemispherical bowl of radius 13 m, shown here in profile. Answer the following questions, given that the volume of water in a hemispherical bowl of radius R is when the water is y meters deep.
a. At what rate is the water level changing when the water is 8 m deep?
b. What is the radius r of the water’s surface when the water is y m deep?
c. At what rate is the radius r changing when the water is 8 m deep?
ANSWER:
Solution:
Step 1:
In this question we have to find out (a) rate of change of water level (b) the radius as a function of water level (c) rate of change of radius when the water level is .
