(a)
The area of the
(a)
Answer to Problem 37E
The area of the square is 2.
Explanation of Solution
Given information:
The Area of a Circle is inscribed at a regular n-sided polygon inside a circle of radius 1.
Formula used:
Calculation:
Since diameter of circle is diagonal of square.
Now,
So,
Conclusion:
The area of the square is 2.
(b)
The area of the polygon for the n=8(octagon).
(b)
Answer to Problem 37E
The total area of octagon is 2.828.
Explanation of Solution
Given information:
The Area of a Circle is inscribed at a regular n-sided polygon inside a circle of radius 1.
Formula used:
Calculation:
Octagon is a collection of 16 right angle triangles with radius of circle as hypotenuse. And one angle of triangle is
So,
Conclusion:
The total area of octagon is 2.828
(c)
The area of the polygon for the n=16.
(c)
Answer to Problem 37E
The total area of octagon is 3.061.
Explanation of Solution
Given information:
The Area of a Circle is inscribed at a regular n-sided polygon inside a circle of radius 1.
Formula used:
Calculation:
16-gon is a collection of 32 right angle triangles with radius of circle as hypotenuse. And one angle of triangle is
So,
Conclusion:
The total area of octagon is 3.061
(d)
The comparison of the area for different n values.
(d)
Answer to Problem 37E
Each area is smaller than area or circle as n increases towards infinity area approaches to area or circle.
Explanation of Solution
Given information:
The Area of a Circle is inscribed at a regular n-sided polygon inside a circle of radius 1.
Formula used:
Calculation:
Area of circle is calculate as
Each area is smaller than area or circle as n increases towards infinity area approaches to area or circle.
Conclusion:
Each area is smaller than area or circle as n increases towards infinity area approaches to area or circle.
Chapter 6 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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