Question

The adjacent figure shows two arcs P and Q. Arc P is part of the circle with centre O and radius OA. Arc Q is a part of the circle with centre M and radius AM, where M is the mid-point of AB. Area enclosed by the arc P is

• A. $51.2c{m}^2$
• B. $52.3c{m}^2$
• C. $53.4c{m}^2$
• D. $54.5c{m}^2$

Answer 1

The correct option is B $52.3c{m}^2$

In $\Delta OMA$, we have
sin $\theta =\frac{AM}{QA}=\frac{5}{10}=\frac{1}{2}$
$\Rightarrow \theta ={30}^{\circ }\therefore \angle AOB=2\times \theta ={60}^{\circ }$

Area enclosed by arc P
=Area of sector of angle ${60}^{\circ }$
$=\frac{\pi r^2\times {60}^{\circ }}{{360}^{\circ }}=\frac{\pi r^2}{6}=\frac{3.14\times 10\times 10}{6}$
$=52.3c{m}^2$