Question

The ratio of the areas of a circle and an equilateral triangle whose diameter and a side are respectively equal, is
(a)π:√2
(b)π:√3
(c)√3:π
(d)√2:π

Answer 1

Answer:

The Ratio of the Areas of circle and equilateral ∆ is π : √3 .

Among the given options option (b) π : √3 is the correct answer.

Step-by-step explanation:

Let ‘r’ be the radius of a circle and ‘a’ be the side of a square.

Given :  

Let ‘d’ be the diameter of a circle and ‘a’ be the side of a equilateral triangle.

Diameter of a circle =  side of equilateral triangle

d = a

Radius of a circle, r = d/2

Area of circle,A1 = πr²

Area of an equilateral ∆, A2 = √3/4 a²

Ratio of the Area of circle and Area of an equilateral ∆  :

A1 : A2  = πr² : √3/4× a²

A1 / A2  = πr² / √3/4 ×a²

A1 / A2  = π(d/2)² / √3/4× a²

A1 / A2  = π(a/2)² / √3/4 ×  a²

[d = a]

A1 / A2  = π(a²/4) / √3/4 × a²

A1 / A2  = πa²/4 ×  4 /√3a²

A1 / A2 = π/√3

A1 :  A2 = π : √3

Hence, the Ratio of the Areas of circle and equilateral ∆ is π : √3 .

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Solution:

Let diameter of a circle = d

Side of an equilateral triangle

= a

And

d = a [ given ] ---(1)

Now ,

ratio = (Area of circle)/(area equilateral triangle )

= [ (πd²)/4 ]/[(√3/4)a²]

= [ πd²/4 ]/[(√3d²/4)]

/* from (1)*/

After cancellation, we get

= π/√3

= π : √3

Therefore,

Option (b) is correct.

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