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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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?

Similar Questions

In $\triangle ABC$,$\angle A = 90^{\circ}$ and $AD \perp BC$,where $D$ lies on $BC$. If $BC = 8 \ cm$ and $AC = 6 \ cm$,then the ratio of the area of $\triangle ABC$ to the area of $\triangle ACD$ is:

The area of a circle is $154 \, cm^{2}$. The length of an arc of the circle which subtends an angle of $45^{\circ}$ at the centre is......$cm$.

The length of one pair of opposite sides of a square is increased by $5 \, cm$ on each side,the ratio of the length and the breadth of the newly formed rectangle becomes $3:2$. What is the area of the original square? (in $cm^2$)

The perimeter of a square is double the perimeter of a rectangle. The area of the rectangle is $240 \, cm^2$. What is the area of the square? (in $cm^2$)

$A$ piece of wire $132 \, cm$ long is bent successively in the shapes of an equilateral triangle,a square,a regular hexagon,and a circle. Then,which has the largest surface area?

Vedclass Test Series

Exam Paper Generator

Online Exam Module