OACB is a quadrant of a circle with center O and radius 3.5 cm. If OD

1.	OACB is a quadrant of a circle with center O and radius 3.5 cm. If OD = 2 cm, find the area of the (i) quadrant OACB (ii) shaded region.
Answer» Given, Radius of small quadrant, r = 2 cm Radius of big quadrant, R = 3.5 cm (i) Area of quadrant OACB = 1/4 πR² = 1/4 (22/7)(3.5)² = 269.5/28 = 9.625 cm² (ii) Area of shaded region = Area of big quadrant – Area of small quadrant = 1/4 π(R² – r²) = 1/4 (22/7)(3.5² – 2²) = 1/4 (22/7)(12.25 – 4) = 1/4(22/7)(8.25) = 6.482 cm²

OACB is a quadrant of a circle with center O and radius 3.5 cm. If OD = 2 cm, find the area of the (i) quadrant OACB (ii) shaded region.

Answer»

Given,

Radius of small quadrant, r = 2 cm

Radius of big quadrant, R = 3.5 cm

(i) Area of quadrant OACB = 1/4 πR²

= 1/4 (22/7)(3.5)²

= 269.5/28 = 9.625 cm²

(ii) Area of shaded region = Area of big quadrant – Area of small quadrant

= 1/4 π(R² – r²)

= 1/4 (22/7)(3.5² – 2²)

= 1/4 (22/7)(12.25 – 4)

= 1/4(22/7)(8.25)

= 6.482 cm²