What is the ratio of the areas of the incircle and circumcircle of a square?
Answer & explanation
Correct answer: option 4
Incircle area square : Circumcircle area of square
In case of Incircle square, the diameter of circle will be side of square.
Thus Area of Circle A1 = Π * Side^2
In case of Circumcircle square, the diameter of circle will be diagonal of square.
$Diagonal^2 = Side^2 + Side^2$
Diagonal = sqrt(2*Side^2) = sqrt(2) * Side
Thus area of circle A2 = Π * diagonal^2 = Π * (sqrt(2) * Side)^2 = 2 Π Side^2
A1:A2 = Π Side^2 : 2Π Side^2 = 1:2
The correct answer is Option (4) → $1: 2$