   Chapter 4.7, Problem 39E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 32 inches, what diameter pizza will reward you with the largest slice?

To determine

To find: The diameter of the pizza.

Explanation

Given:

The perimeter of the slice is 32 in .

Calculation:

Let the radius of the pizza be r and the angle of the pizza is θ

From Figure 1, the arc length of the slice of the pizza is S=rθ .

The area of the pizza slice is A=θ2r2 .

Hence, perimeter of the slice is, θr+r+r=(θ+2)r .

Therefore,

(θ+2)r=32θ+2=32rθ=32r2

Substitute θ=32r2 in A=θ2r2 ,

A=(32r2)2r</

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