Question : The ratio of the area of a square and that of a circle, when the length of a side of the square is equal to that of the diameter of the circle, is:
( $\pi =\frac{22}{7}$ )

Option 1: 14 : 11

Option 2: 28 : 11

Option 3: 7 : 22

Option 4: 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:

Option 1: $\sqrt\pi:1$

Option 2: $1:\sqrt\pi$

Option 3: $(\pi)^2:1$

Option 4: $1:\sqrt2\pi$

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:

Option 1: $2\pi :1$

Option 2: $1:\sqrt{\pi}$

Option 3: $\sqrt{\pi}:1$

Option 4: $1:\pi$

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: $(\sqrt{2}-1)$

Question : The circumference of a circle is equal to the perimeter of an equilateral triangle. If the radius of the circle is 7 cm, what is the length of the side of the equilateral triangle?

Option 1: $\frac{22}{3}$ cm

Option 2: $\frac{44}{3}$ cm

Option 3: $44$ cm

Option 4: $22$ cm

Question : The length of a side of an equilateral triangle is 8 cm. The area of the region lying between the circumcircle and the incircle of the triangle is __________ ( Use: $\pi = \frac{22}{7}$)

Option 1: $50\frac{1}{7}\ \text{cm}^2$

Option 2: $50\frac{2}{7}\ \text{cm}^2$

Option 3: $75\frac{1}{7}\ \text{cm}^2$

Option 4: $75\frac{2}{7}\ \text{cm}^2$