Question

OACB is a quadrant of a circle with centre O and radius 7 cm. If OD = 4 cm, then find the area of the shaded region.

• A. 18.5 $c{m}^2$
• B. 20.5 $c{m}^2$
• C. 22.5 $c{m}^2$
• D. 24.5 $c{m}^2$

Answer 1

The correct option is D 24.5 $c{m}^2$

For the quadrant $\theta ={90}^{\circ }$
Area of the quadrant $=\frac{\theta }{{360}^{\circ }}\times \pi (r{)}^2$

Area of quadrant OACB = $\frac{{90}^{\circ }}{{360}^{\circ }}\times \frac{22}{7}\times (7{)}^2=\frac{77}{2}$

Area of shaded region = Area of quadrant OACB - Area of $△$OAD

$=\frac{77}{2}-\frac{1}{2}\times 7\times 4$

$=24.5c{m}^2$