To calculate: The area of the region that lies outside the circle
Answer to Problem 111E
The area of the region is
Explanation of Solution
Given information:
Equations of two circles
Formula used:
Standard equation of a circle passing through center
Area of a circle with radius r units is product of pi
Calculation:
Consider the provided equations of
Recall the standard equation of a circle passing through center
Comparing
Now, convert
Comparing
Now, plot both the circle on the coordinate plane as,
Area of the region that lies outside the circle
Recall area of a circle with radius r units is product of pi
So, area of bigger circle with radius 4 units is calculated as,
Area of smaller circle with radius 2 units is calculated as,
Now, area of the region that lies outside the circle
Thus, the area of the region is
Chapter 1 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning