Concept explainers
a.
To find the speed of the water level falling when the radius is
a.
Answer to Problem 17E
The water level is decreasing by
Explanation of Solution
Given information:
Water is flowing at the rate of
Formula:
Graph:
Let the height be
Rate of volume change,
Volume of cone is
Substitute for
Differentiate
At the moment
Therefore, the water level is decreasing by
b.
To Find:
To find the change in radius of water’s surface.
b.
Answer to Problem 17E
The change in radius is decreased by
Explanation of Solution
Given information:
Water is flowing at the rate of
Formula:
From part (a), we have
The relationship between the height and radius is based on the cones dimension,
On differentiating we get,
Therefore, the change in radius is decreased by
Chapter 5 Solutions
Calculus: Graphical, Numerical, Algebraic
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