Question

If a square is inscribed in a circle, what is the ratio of the area of the circle and the square?

Answer 1

SOLUTION:
FIGURE IS IN THE ATTACHMENT.

Let ABCD be a square inscribed in a circle of radius ‘r’. OA =OB= OC = OD = r
Diagonal AC = OA + OC = r + r = 2r

Let ‘a’ be the length of a side of the square.
Diagonal of  Square (AC) = √2 × side = √2a
√2a = 2r

a = 2r/√2 =( 2r × √2) / (√2×√2) = 2√2r/2= √2r
[Rationalising the denominator]
a = √2r

Area of a square = side² = a² = (√2r)²= 2r²
Area of circle = πr²

Area of circle : Area of a square
πr² : 2r²
π : 2

Hence, the ratio of the area of the circle and the square is π : 2.

HOPE THIS WILL HELP YOU...