Concept explainers
a.
To find: how fast is the level in the pot rising when the coffee in the cone in 5 inch deep.
a.
Answer to Problem 42E
The value of
Explanation of Solution
Given information:
From the given diagram, we can see that the conical diameter is 6, cylindrical coffee pot diameter is 6 and the conical filter height is 6.
Calculation :
We have to calculate how fast is the level in the pot rising when the coffee in the cone in 5 inch deep.
Therefore,
Volume of a cylindrical coffee pot is
Since radius is constant, we put
Differentiate with respect to t .
Putting the value of
Hence, the value of
b.
To find: how fast is the level in the cone falling.
b.
Answer to Problem 42E
The value of
Explanation of Solution
Given information:
From the given diagram, we can see that the conical diameter is 6, cylindrical coffee pot diameter is 6 and the conical filter height is 6.
Calculation :
We have to calculate how fast is the level in the cone falling.
Therefore,
Volume of a cone filter is
We use similar triangles of a cone.
We get
Putting the value of
Differentiate with respect to t .
Putting the value of
Hence, value of
Chapter 5 Solutions
Calculus: Graphical, Numerical, Algebraic
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