Question

A Circle Is made inside and outside of a regular hexagon of given length .Find Ratio of area of two circles .

Answer 1

Answer:

4 : 3

Step-by-step explanation:

A Circle Is made inside and outside of a regular hexagon of given length .Find Ratio of area of two circles .

in hexagon angles between adjacent sides = 120°

if we form a triangle with center from any side

angle would be 120/2 = 60°

Hence Equilateral Triangle

Line from center to corner of one side of Hexagon would be radius of external circle and equal to sides of hexagon.

Lets call it  = R

Then Radius of internal circle would be equal to ⊥ on a any side from center point .

r² = R² - (R/2)²  = 3R² / 4

Area of external circle = π R²

Area of internal circle = πr² =  π3R² / 4

Area of external circle : Area of internal circle :: 4 : 3