Question : The ratio of the area of an equilateral triangle and that of its circumcircle is:

Option 1: $2\sqrt3:2\pi$

Option 2: $4:\pi$

Option 3: $3\sqrt3:4\pi$

Option 4: $7\sqrt2:2\pi$

Question : The ratio of the area of a regular hexagon and an equilateral triangle having the same perimeter is:

Option 1: $2:3$

Option 2: $6:1$

Option 3: $3:2$

Option 4: $1:6$

Question : The area of a square is 1296 cm² and the radius of a circle is $\frac{7}{6}$ of the length of a side of the square. What is the ratio of the perimeter of the square and the circumference of the circle? [Use $\pi=\frac{22}{7}$ ]

Option 1: 13 : 11

Option 2: 8 : 11

Option 3: 6 : 11

Option 4: 3 : 7

Question : Nine times the area of a circle is the same as the three times the area of a square. What is the ratio of the diameter of the circle and the diagonal of the square?

Option 1: $\sqrt{2}: \sqrt{3 \pi}$

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

Option 3: $2: 3 \pi$

Option 4: $\sqrt{5}: \sqrt{7 \pi}$

Question : If the circumference of a circle is equal to the perimeter of a square, and the radius of the given circle is positive, then which of the following options is correct?

Option 1: Area of the circle > Area of the square

Option 2: Area of the circle $\geq$ Area of the square

Option 3: Area of the circle < Area of the square

Option 4: Area of the circle = Area of the square