Question

Find a polynomial for the sum of the shaded areas of the figure. A = 6, B = 4

Answer 1

Answer:

The polynomial for the sum of the shaded  $\pi$ r² - 20 $\pi$

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 $\pi$ R , where R is the radius

So, for circle with radius B.

The circumference = 2 $\pi$ R = 2 $\pi$ B

Or, The circumference = 2 $\pi$ × 4 = 8 $\pi$

Similarly

For circle with radius A.

The circumference = 2 $\pi$R = 2 $\pi$ A

Or, The circumference = 2 $\pi$ × 6 = 12 $\pi$

Now, The area of circle with radius r is

Area = $\pi$ ×radius × radius

Or, Area = $\pi$ 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 =  $\pi$ r² - ( 8 $\pi$ + 12 $\pi$ )

Or,  The sum of shaded region area =  $\pi$ r² - 20 $\pi$

Hence The polynomial for the sum of the shaded area is $\pi$ r² - 20 $\pi$  Answer