Geometry

Circles

Medium

When a particular wire is bent into the shape of a square, then the area of the square turns out to be $81cm^2$ . When the same wire is bent into a circle, then the radius of the circle (correct to two decimal places) is

2.86

5.73

11.46

✅ Correct Option: 2

The wire is bent into a square with area $81 \text{ cm}^2$ .

Area of square $= (\text{side})^2$

$(\text{side})^2 = 81$

$\text{side} = \sqrt{81} = 9 \text{ cm}$

The perimeter of the square equals the length of the wire.

Perimeter of square $= 4 \times \text{side}$

Length of wire $= 4 \times 9 = 36 \text{ cm}$

When the same wire is bent into a circle, the length of the wire equals the circumference of the circle.

Circumference $= 2\pi r$

$2\pi r = 36$

$r = \dfrac{36}{2\pi}$

$r = \dfrac{18}{\pi}$

$r = \dfrac{18}{3.14159}$

$r = 5.729...$

$r \approx 5.73 \text{ cm}$

Therefore, the radius of the circle is $5.73 \text{ cm}$ .

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When a particular wire is bent into the shape of a square, then the area of the square turns out to be 81cm281cm^281cm2. When the same wire is bent into a circle, then the radius of the circle (correct to two decimal places) is

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CUET General Test Past Year Questions (Topic-Wise)

When a particular wire is bent into the shape of a square, then the area of the square turns out to be $81cm^2$ . When the same wire is bent into a circle, then the radius of the circle (correct to two decimal places) is