Question

In the given figure below, OACB is a quadrant of a circle. The radius OA = 3.5 cm, OD = 2 cm. Calculate the area of the shaded region.

• A. 6.5 $c{m}^2$
• B. 6.125 $c{m}^2$
• C. 7 $c{m}^2$
• D. 5.125 $c{m}^2$

Answer 1

The correct option is B 6.125 $c{m}^2$

Area of a quadrant of a circle = $\frac{1}{4}\times$ area of the circle.
$\therefore$ Area of the shaded region = $\frac{1}{4}\times$ Area of the circle - Area of the triangle.
$⟹$ Area of the shaded region = $\frac{1}{4}\times \pi r^2$ $-\frac{1}{2}base\times height$
$⟹$ Area of the shaded region = $\frac{1}{4}\times \frac{22}{7}\times 3.5\times 3.5$ $-\frac{1}{2}\times 3.5\times 2$
$⟹$ Area of the shaded region = 9.625 - 3.5 = 6.125 $c{m}^2$