Question

The radius of the circle given above is 7cm and the angle subtended by the arc is ${60}^{\circ }$. If the area of $\Delta$OAB is $21{cm}^2$, then the area of segment APB is___ .(Take the value of $\pi$ as $\frac{22}{7}$)

• A. $5.8{cm}^2$
• B. $4.7{cm}^2$
• C. $8{cm}^2$
• D. $1{cm}^2$

Answer 1

The correct option is B $4.7{cm}^2$

$\text{Area of sector OAPB}=\frac{60}{360}\times \pi r^2=\frac{60}{360}\times \frac{22}{7}\times 7^2=25.7{cm}^2\text{Area of segment APB = Area of sector OAPB - Area of triangle OAB}=25.7-21=4.7{cm}^2$

$\text{Therefore, area of segment APB}=4.7{cm}^2$