Question

The ratio of the areas of a circle and an equilateral triangle whose diameter and a side are respectively equal, is

(a) $\mathrm{\pi }:\sqrt{2}$

(b) $\mathrm{\pi }:\sqrt{3}$

(c) $\sqrt{3}:\mathrm{\pi }$

(d) $\sqrt{2}:\mathrm{\pi }$

Answer 1

We are given that diameter and side of an equilateral triangle are equal.

Let d and a are the diameter and side of circle and equilateral triangle respectively.

We know that area of the circle

Area of the equilateral triangle

Now we will find the ratio of the areas of circle and equilateral triangle.

We know that radius is half of the diameter of the circle.

Now we will substitute in the above equation,

Therefore, ratio of the areas of circle and equilateral triangle is.

Hence, the correct answer is option (b).