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 : The side of an equilateral triangle is 9 cm. What is the radius of the circle circumscribing this equilateral triangle?

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

Option 2: $5\sqrt{3}$ cm

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

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

Question : The circumference of a triangle is 24 cm and the circumference of its in-circle is 44 cm. Then the area of the triangle is (taking $\pi =\frac{22}{7}$):

Option 1: 56 sq. cm

Option 2: 84 sq. cm

Option 3: 48 sq. cm

Option 4: 68 sq. 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: $75\frac{2}{7}\ \text{cm}^2$

Question : The side of an equilateral triangle is 12 cm. What is the radius of the circle circumscribing this equilateral triangle?

Option 1: $6 \sqrt{3}\ \text{cm}$

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

Option 3: $9 \sqrt{3}\ \text{cm}$

Option 4: $5\sqrt{3}\ \text{cm}$