Question : A circle is inscribed in an equilateral triangle and a square is inscribed in that circle. The ratio of the areas of the triangle and the square are:

Option 1: $\sqrt3:4$

Option 2: $\sqrt3:8$

Option 3: $3\sqrt3:2$

Option 4: $3\sqrt3:1$

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 : 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 : The perimeter of an equilateral triangle is 40 cm more than the length of each of its sides. What is the length of each side of this equilateral triangle?

Option 1: 10 cm

Option 2: 30 cm

Option 3: 15 cm

Option 4: 20 cm

Question : The curved surface area is thrice as big as the base area of a cone. If the diameter of the cone is 1 cm. Then what is the total surface area (in cm²) of the cone?

Option 1: $\pi$

Option 2: $3\pi $

Option 3: $2\pi$

Option 4: $4\pi $