Question

With centre O, quadrants of 2 circles are drawn. If OA = 5 cm, AB = 7 cm, find the area of the shaded region. `["Take"  π = 22/7]`

Answer 1

Given:

• Centre O, two circle quadrants are drawn.
• OA = 5 cm   ...(Radius of smaller quadrant)
• AB = 7 cm   ...(Difference in radius between larger and smaller)
• `π = 22/7`

Step-wise calculation:

1. Radius of smaller quadrant = OA = 5 cm

2. Radius of larger quadrant = OA + AB = 5 + 7 = 12 cm

3. Area of larger quadrant 

= `1/4 xx π xx 12^2` 

= `1/4 xx 22/7 xx 144` 

= `(22 xx 144)/(4 xx 7)` 

= `3168/28` 

= 113.14 cm²   ...(Approx)

4. Area of smaller quadrant 

= `1/4 xx π xx 5^2` 

= `1/4 xx 22/7 xx 25` 

= `(22 xx 25)/(4 xx 7)` 

= `550/28` 

= 19.64 cm²   ...(Approx)

5. Area of shaded region 

= Area of larger quadrant – Area of smaller quadrant 

= 113.14 – 19.64

= 93.5 cm²   ...(Approx)

The area of the shaded region is approximately 93.5 cm².