Question

Figure represents a quadrant of a circle of radius 3.5 cm with centre O. 

1. Calculate the area of the quadrant OACB. 
2. Given OD = 2 cm, calculate the area of the shaded region `("Take"  π = 22/7)`.

Answer 1

Step 1: Calculate the area of quadrant OACB

The area of a quadrant is given by the formula `1/4 πr^2`.

Given that the radius r = 3.5 cm = `7/2` cm and `π = 22/7`.

Area of quadrant OACB = `1/4 xx 22/7 xx (7/2)^2`

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

Area = `(11 xx 7)/8`

= `77/8` cm²

= 9.625 cm²

Step 2: Calculate the area of ΔAOD

In the right-angled triangle AOD, the base AO is the radius of the quadrant 3.5 cm and the height OD is given as 2 cm.

Area of ΔAOD = `1/2` × base × height

Area = `1/2 xx 3.5 xx 2`

= 3.5 cm²

Step 3: Calculate the area of the shaded region

The area of the shaded region is the difference between the area of the quadrant OACB and the area of ΔAOD.

Area of shaded region = Area of quadrant OACB – Area of ΔAOD

Area = 9.625 – 3.5

= 6.125 cm²

i. The area of the quadrant OACB is 9.625 cm².

ii. The area of the shaded region is 6.125 cm².