Question

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

Answer 1

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

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