Question

Find the shaded area in the given circle with radius 20 cm, ∠AOB = 90°. [Take π = 3.14]

Answer 1

Given:

• Radius of the circle, r = 20 cm
• Central angle, ∠AOB = 90°
• π = 3.14

Step-wise calculation:

1. Calculate the area of the sector with central angle 90°:

Area of sector = `θ/360^circ xx πr^2`

= `90/360 xx 3.14 xx 20^2`

= `1/4 xx 3.14 xx 400`

= 314 cm²

2. Calculate the area of the triangle ΔAOB which is an isosceles right triangle as ∠AOB = 90°: 

Area of ΔAOB = `1/2 xx OA xx OB`

= `1/2 xx 20 xx 20`

= 200 cm²

3. Calculate the shaded area, which is the area of the sector minus the area of the triangle:

Shaded area = Area of sector – Area of ΔAOB

= 314 – 200

= 114 cm²

The shaded area in the circle with radius 20 cm and angle 90° at the center is 114 cm².