Question

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

• A. $5c{m}^2$
• B. $6c{m}^2$
• C. $8c{m}^2$
• D. $10c{m}^2$

Answer 1

The correct option is B

$6c{m}^2$

Radius of the quadrant $=3.5cm=\frac{7}{2}cm$
Area of triangle BOD $=\frac{1}{2}\times \frac{7}{2}\times 2c{m}^2$
$=\frac{7}{2}c{m}^2$
Area of shaded region = Area of quadrant - Area of triangle BOD
$=(\frac{77}{8}-\frac{7}{2})c{m}^2=\frac{49}{8}c{m}^2$
$=6.125c{m}^2$ ~ $6c{m}^2$