Concept explainers
a.
To determine rate of the water level changing when the water is
a.
Answer to Problem 18E
The water level is decreasing by
Explanation of Solution
Given information:
Water is flowing at the rate of
Formula:
The bowl radius is
Hemisphere volume when water is
Rate of water flow is negative as it is flowing out,
Differentiate
At the moment the water is
Therefore, the water level is decreasing by
b.
To Find:
To find the radius of water’s surface when the water is
b.
Answer to Problem 18E
The radius is found to be
Explanation of Solution
Given information:
Water is flowing at the rate of
Formula:
Pythagorean theorem
Binomial theorem
The bowl radius is
Side
Using Pythagorean theorem find
Therefore, the radius is found to be
c.
To Find:
To find the rate of radius changing when the water is
c.
Answer to Problem 18E
The rate of radius is found to be
Explanation of Solution
Given information:
Water is flowing at the rate of
Formula:
From part (b), we have
Implicitly differentiating to derive
Therefore, the rate of radius is found to be
Chapter 5 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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