If the circumference of a circle and the peri | vedclass

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Question

(A) Let the radius of the circle be $r$ and the side of the square be $a$.
According to the given condition,the circumference of the circle equals th

Vedclass · Accepted Answer

Area of the circle $>$ Area of the square

Vedclass · Answer

(A) Let the radius of the circle be $r$ and the side of the square be $a$.
According to the given condition,the circumference of the circle equals the perimeter of the square:
$2 \pi r = 4a$
$\pi r = 2a$
$a = \frac{\pi r}{2}$
Now,the area of the circle is $A_1 = \pi r^2$.
The area of the square is $A_2 = a^2 = (\frac{\pi r}{2})^2 = \frac{\pi^2 r^2}{4}$.
Comparing $A_1$ and $A_2$:
$\frac{A_1}{A_2} = \frac{\pi r^2}{\frac{\pi^2 r^2}{4}} = \frac{4}{\pi}$.
Since $\pi \approx 3.14$,$\frac{4}{3.14} > 1$.
Therefore,$A_1 > A_2$,which means the area of the circle is greater than the area of the square.

If the circumference of a circle and the perimeter of a square are equal,then

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