Question : Two equal circles intersect so that their centres and the points at which they intersect form a square of side 1 cm. The area (in cm2) of the portion that is common to the circle is:
Option 1: $\frac{\pi }{4}$
Option 2: $\frac{\pi }{2}-1$
Option 3: $\frac{\pi }{5}$
Option 4: $(\sqrt{2}-1)$
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: $\frac{\pi }{2}-1$
Solution :
Given: The side of the square = 1 cm The area of the square = $\operatorname{(side)^2}$ $A_{\text{square}}= 1$ cm 2 The radius of each circle = 1 cm The angle of the sector = $\frac{\pi}{2}$ The area of the sector = $\frac{\theta}{360^{\circ}}×\pi r^2$ $ A_{\text{sector}} = \frac{90^{\circ}}{360^{\circ}}×\pi (1)^2 = \frac{\pi}{4} $ cm 2 The area of the portion that is common to the two circles, $2A_{\text{sector}} - A_{\text{square}} = \frac{2\pi}{4} - 1 =\frac{\pi}{2} - 1$. Hence, the correct answer is $\frac{\pi}{2} - 1$.
Candidates can download this ebook to know all about SSC CGL.
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Question : Four circles of equal radii are described around the four corners of a square so that each touches two of the other circles. If each side of the squares is 140 cm, then the area of the space enclosed between the circumference of the circle is: (Take $\pi=\frac{22}{7}$)
Question : A circle and a square have the same area. The ratio of the side of the square to the radius of the circle will be:
Question : Two identical circles each of radius 30 cm intersect each other such that the circumference of each one passes through the centre of the other. What is the area of the intersecting region?
Question : The areas of a circle and a square are the same. The ratio of the side of the square to the radius of the circle is:
Question : A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. The area of the circle is: (take $\pi=\frac{22}{7}$)
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile