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Chapter 7.P, Problem 1P
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Calculus (MindTap Course List)
8th Edition
James Stewart
ISBN: 9781285740621
BuyFindarrow_forward
Calculus (MindTap Course List)
8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem
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Three mathematics students have ordered a 14-inch pizza. Instead of slicing it in the traditional way, they decide to slice it by parallel cuts, as shown in the figure. Being mathematics majors, they are able to determine where to slice so that each gets the same amount of pizza. Where are the cuts made?
To determine
To find:
Where are the cuts are made on the 14-inch pizza to obtain 3 same pizza pieces.
Answer
Solution:
The slicing distance is 1.85 inch from the centre.
Explanation
Given:
Pizza size is 14 inch.
Radius of the pizza be R which is 7 inch.
Decided to be cut in parallel way.
Each of the three student to get same amount of pizza piece.
Let the radius of the pizza be R which is 7 inch.
The distance of any general strip from the centre be r,
Length of the strip
Width of the strip dr
Area of the strip
Let distance of the slicing from the centre be d,
Integrating from d to R we shall get the area of slice. But it is one third of total area so it is
Thus we have
Conclusion:
The slicing distance is 1.85 inch from the centre.
Chapter 7 Solutions
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