Question

In the following figure, three sectors of a circle of radius 5 cm, making angles 35°, 50° and 95° at the centre are shaded. Find the area of the shaded region. `("Use"  π = 22/7)`

Answer 1

Given: Circle with radius r = 5 cm; three shaded sectors have central angles 35°, 50° and 95° (sum = 180°). Use `π = 22/7`.

Step-wise calculation:

1. Sum of shaded angles = 35° + 50° + 95°

= 180°

2. Area of a sector = `(θ/360) xx π r^2`. 

For the shaded region (combined)

Area = `(180/360) xx π xx 5^2`

= `(1/2) xx π xx 25`

= `(25/2)π cm^2`

3. Substitute `π = 22/7`: 

Area = `(25/2) xx (22/7)` 

= `(25 xx 11)/7` 

= `275/7 cm^2`

4. As a mixed number / decimal:

`275/7 = 39 2/7 ≈ 39.2857 cm^2`

Required shaded area = `(25/2)π cm^2`

= `275/7` cm² ≈ 39.29 cm²