Question

In the given figure, OACB is a quadrant of a circle with centre O and radius 7 cm. If OD = 4 cm, then find the area of shaded region.
(Use $\pi$ = $\frac{22}{7}$)

• A. 32 $c{m}^2$
• B. 19 $c{m}^2$
• C. 34 $c{m}^2$
• D. 24.5 $c{m}^2$

Answer 1

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

For the quadrant $\theta =90°$
Area of the quadrant = $\frac{\theta }{360°}\times \pi (r{)}^2$
Area of quadrant OACB
= $\frac{90}{360}$ $\times$ $\frac{22}{7}$ $\times$ $(7{)}^2$ = $\frac{77}{2}$

Area of shaded region = Area of quadrant OACB - area of $\Delta$OAD

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

= 24.5 $c{m}^2$