The area of the shaded region.
Answer to Problem 34PPS
The area of the shaded region is 77
Explanation of Solution
Given: Two
Concept Used: The formula for the area of circle with radius r is given by-
Area of circle
The area of any shaded region can be found by subtracting the total unshaded region from the total region.
Calculations: The total region in this case is the larger circle whose diameter is 14 mm.
Hence, radius of the larger circle will be equal to-
Radius =
Thus, area of the total region is given by-
Total area
The unshaded region consists of two circles enclosed within the larger circle. From the figure it is clear that the both the unshaded circles are congruent and the sum of the diameters of both the circles is equal to the diameter of the larger circle. Let the diameter of both the unshaded circles be d.
Thus,
Hence, the diameter of each small circle is 7
Radius =
Therefore total area of the unshaded region is given by-
Total unshaded area
Thus, the area of the shaded region is given by-
Shaded area
Thus, total shaded area is
Chapter 11 Solutions
Geometry, Student Edition
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PREALGEBRA
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning