Question

if the circumference of a circle and the perimeter of a square are equal then find the relation between area of circle and area of square ​

Answer 1

Let radius of circle = x
Let side of square = y

Then
4 y = 2 x pi x X
y = ( 1/2 pi ) x

Area circle = pi x X2

Area of square = y2
= ( 1/2 pi )2 x X2
= 1/4 x pi x pi x X2
= ( 1/4 pi ) ( pi x X2)
= pi /4 ( area of circle )

Relation:
Area square = 3.14/4 x area of circle
Area square = 0.8 x area of circle ( approx)

Answer 2

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let x be the perimeter and circumference of square and circle

then perimeter of square = x

4 side = x

side = x/4

and also circumference of the circle = x

2 r = x

2 * 22/7 * r = x

r = 7x/44

area of square (S) = side^2 = (x/4)^2 = x^2/16

area of the circle(c) = r^2 = 22/7 * (7x/44)^2 = 7x^2/88

so (S) , (c) =

x^2/16 , 7x^2/88 LCM of 16 and 88 = 176

S = x^2/16 * 11/11 = 11x^2/176

C = 7x^2/88 * 2/2 = 14x^2/176

so here 11x^2/176 < 14x^2/176

so , S < C

Area of the circle > Area of the square

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