Finding Area Of Shaded Portions Of A Circle

Introduction to Area of Shaded portion of the circle:

Finding area of a shaded portion of a circle region is a fraction of the area of the circle. This area is proportional to the angle of the shaded region. In other words, the larger the angle, the larger is the area of the shaded region.

We know that the area of the circle is = π * r2

where π = 3.14

The area of the shaded portion of the circle is = `theta` / 360 *area of the circle where  is angle of the shaded region.

Finding area of a shaded portion of a circle has shown:

Find the area of the shaded portion in given diagram:

Given diagram outer circle diameter is 12 and the inner circle diameter is 6

circle

solution: Given that the diameter of the circle 1 = 12cm

diameter of the circle 2 = 6cm

Area of the circle = `pi`r2

diameter of circle 1  = 12

radius of circle 1 = d / 2              [d = diameter]

radius of circle 1 = 12 / 2 = 6

diameter of circle 2 = 6

radius of circle 2 = d / 2             [d = diameter]

radius of circle 2 = 6 / 2 = 3

Area of the given shaded portion = `pi`r2 - `pi`r2

= 3.14 (62) – 3.14(32)          [`pi` = 3.14]

= 3.14 * 36   – 3.14 * 9

= 113.04 – 28.26

= 84.78

solution is 84.78.

Finding the area of a shaded portion of a circle problems:

Example of the shaded portion of a circle:

circle

solution:

Given that circle = 10 radius

square = 4cm

Area of the circle = `pi` r2

Area of the square = a2

Find the are the shaded portion =  area of the circle – area of the square

= `pi` r- a2

`pi` = 3.14

r = 10cm

a = 4

= 3.14 ( 102) – 42

= 3.14 *100  -  16

= 298

solution is = 298.

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