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15 Nov 2021
Problem 27
Page 306
Section 4.6: Optimization Problems
Chapter 4: Applications of Differentiation
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15 Nov 2021
Given information
A cup which is made from a circular piece of paper of radius by cutting out a sector and joining the edge and .
Step-by-step explanation
Step 1.
The radius of the cone shaped drinking cup is and the height is .
In the figure, in tringle by Pythagoras theorem,
Volume
Substitute the value of in
Differentiate with respect to
For critical points,
Since the height cannot be negative, reject