Question

OACB is a quadrant of a circle of radius 3.5 cm with centre O. If OD = 2 cm, calculate the area of the shaded region.

Answer 1

Given:

• Quadrant OACB of circle radius r = 3.5 cm.
• OD = 2 cm perpendicular distance from O to chord AD.
• Need to find the shaded area bounded by arc AC and chord AD inside the quadrant.

Shaded Area = Area of Quadrant OACB − Area of Triangle AOD

Step 1: Area of the quadrant

Area of quadrant​ = `1/4 pir^2`

= `1/4 xx 22/7 xx (3.5)^2`

= `1/4 xx 22/7 xx 49/4`

= `(22 xx 49)/112`

= `1078/112 ≈ 9.625  cm^2`

Step 2: Area of triangle AOD

In triangle AOD, it’s a right triangle:

• AO = 3.5cm (radius)
• OD = 2 cm (given)
• Right angle at O

Area of ΔAOD = `1/2 xx AO xx OD`

= `1/2 xx 3.5 xx 2`

= `7/2`

= 3.5 cm²

Step 3: Area of shaded region

Shaded Area = 9.625 − 3.5 = 6.125 cm²