If the circumference of a circle and the perimeter of a square are equal, then ______.
Area of the circle = Area of the square
Area of the circle < Area of the square
Area of the circle > Area of the square
Nothing definite can be said about the relation between the areas of the circle and square.
If the circumference of a circle and the perimeter of a square are equal, then Area of the circle > Area of the square.
Circumference of a circle = Perimeter of square
`2pir = 4a` .....[Where r and a are radius of circle and side of square respectively]
⇒ `22/7 r = 2a`
⇒ `11r = 7a`
⇒ `a = 11/7 r`
⇒ `r = (7a)/11` ......(i)
Now, Area of circle, `A_1 = pir^2`
= `pi((7a)/11)^2 = 22/7 xx (49a^2)/121` .....[From equation (i)]
= `(14a^2)/11` ......(ii)
And Area of square, `A_2 = (a)^2` .....(iii)
From equations (ii) and (iii), `A_1 - 14/11 A_2`
∴ `A_1 > A_2`
Hence, Area of the circle > Area of the square.
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