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: $\frac{π}{4}$
Option 2: $\frac{π}{2} - 1$
Option 3: $\frac{π}{5}$
Option 4: $(\sqrt{2} - 1)$

Question

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 $π = \frac{22}{7}$ )
Option 1: 4200 cm²
Option 2: 2100 cm²
Option 3: 7000 cm²
Option 4: 2800 cm²

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Answer 1

Correct Answer: $\frac{π}{2} - 1$

Solution :

Given: The side of the square = 1 cm
The area of the square = $(side)^{2}$
$A_{square} = 1$ cm ²
The radius of each circle = 1 cm
The angle of the sector = $\frac{π}{2}$
The area of the sector = $\frac{θ}{360^{\circ}} \times π r^{2}$
$A_{sector} = \frac{90^{\circ}}{360^{\circ}} \times π (1)^{2} = \frac{π}{4}$ cm ²
The area of the portion that is common to the two circles,
$2 A_{sector} - A_{square} = \frac{2 π}{4} - 1 = \frac{π}{2} - 1$ .
Hence, the correct answer is $\frac{π}{2} - 1$ .

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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: π4Option 2: π2−1Option 3: π5Option 4: (2−1)

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