Question

A point is chosen in the diagram. Given that the radius of the circle is equal to the half the measure of the side of the square, what is the probability that the chosen point is in the shaded area of the part of the circle?

• A.
  
• B.
  
• C.
  
• D.
  

Answer 1

The correct option is B

Let 'a' be the side of the square. And $\frac{a}{2}$ is the radius of the circle and also the half of the side of the square.
Shaded area $=\frac{3}{4}$ x area of the complete circle (Given that it is square and angle subtended by one quarter is ${90}^{\circ }$)
$=\frac{3}{4}\pi {\left(\frac{a}{2}\right)}^2$
Total area = area of the square + area of the shaded portion
$a^2+\frac{3}{4}\pi {\left(\frac{a}{2}\right)}^2$
Probability that the point lies in the shaded region $=\frac{shadedarea}{totalarea}$
$=\frac{3\pi }{(16+3\pi )}$