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Answer:
The polynomial for the sum of the shaded r² - 20
Step-by-step explanation:
Given as :
The figure is shown which is of concentric circle with radius B , A , r
The radius B = 4 unit
The radius A = 6 unit
Let The sum of shaded portion = x unit
Now, The circumference of circle = 2 R , where R is the radius
So, for circle with radius B.
The circumference = 2 R = 2
B
Or, The circumference = 2 × 4 = 8
<u>Similarly</u>
For circle with radius A.
The circumference = 2 R = 2
A
Or, The circumference = 2 × 6 = 12
Now, <u>The area of circle with radius r is</u>
Area = ×radius × radius
Or, Area = r²
Now,
The sum of shaded region area = The area of circle with radius r - ( The circumference with radius B + The circumference with radius A )
Or, The sum of shaded region area = r² - ( 8
+ 12
)
Or, The sum of shaded region area = r² - 20
Hence The polynomial for the sum of the shaded area is r² - 20
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