The area of a circle is same as the area of a | vedclass

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Question

(C) Let the radius of the circle be $r$ and the side of the square be $a$.Given that the area of the circle equals the area of the square: $\pi r^{2}

Vedclass · Accepted Answer

$\sqrt{2}: \sqrt{\pi}$

Vedclass · Answer

(C) Let the radius of the circle be $r$ and the side of the square be $a$.Given that the area of the circle equals the area of the square: $\pi r^{2} = a^{2}$.Taking the square root on both sides,we get $a = \sqrt{\pi} r$.The diameter of the circle is $D = 2r$.The diagonal of the square is $d = \sqrt{2} a$.Substituting the value of $a$ in the diagonal formula: $d = \sqrt{2} (\sqrt{\pi} r) = \sqrt{2\pi} r$.The ratio of the diameter of the circle to the diagonal of the square is $\frac{D}{d} = \frac{2r}{\sqrt{2\pi} r}$.Simplifying the expression: $\frac{2}{\sqrt{2\pi}} = \frac{\sqrt{2} \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{\pi}} = \frac{\sqrt{2}}{\sqrt{\pi}}$.Thus,the ratio is $\sqrt{2} : \sqrt{\pi}$.

The area of a circle is same as the area of a square. What is the ratio of the diameter of the circle and the diagonal of the square?

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