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 : A square and a regular hexagon are drawn such that all the vertices of the square and the hexagon are on a circle of radius $r$ cm. The ratio of area between the square and the hexagon is:

Option 1: $3: 4$

Option 2: $4:3\sqrt{3}$

Option 3: $\sqrt{2}:\sqrt{3}$

Option 4: $1:\sqrt{2}$

Question : ABCD is a square inscribed in a circle of radius $r$. Then the total area (in square units) of the portions of the circle lying outside the square is:

Option 1: $\pi (r^{2}-4)$

Option 2: $2\pi (r ^{2}-1)$

Option 3: $\pi^{2} r(r-7)$

Option 4: $r^{2}(\pi -2)$

Question : The perimeter of an equilateral triangle is equal to the circumference of a circle. The ratio of their areas is: ( Use $\pi =\frac{22}{7}$)

Option 1: $22 : 21\sqrt{3}$

Option 2: $21: 22\sqrt{3}$

Option 3: $21: 22\sqrt{2}$

Option 4: $22: 21\sqrt{2}$

Question : In a circle of radius 3 cm, two chords of length 2 cm and 3 cm lie on the same side of a diameter. What is the perpendicular distance between the two chords?

Option 1: $\frac{4 \sqrt{3}-3 \sqrt{2}}{2}$ cm

Option 2: $\frac{4 \sqrt{2}-3 \sqrt{3}}{2}$ cm

Option 3: $\frac{4 \sqrt{2}-3 \sqrt{3}}{3}$ cm

Option 4: $\frac{4 \sqrt{2}-3 \sqrt{3}}{4}$ cm