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A man has bent a circular wire of radius $49\text{cm}$ to form a square. Find the sides of a square. $\newline$ $100\text{cm}$ $\newline$ $50\text{cm}$ $\newline$ $98\text{cm}$

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Circles: word problems

Full solution

Q. A man has bent a circular wire of radius

49\text{cm}

to form a square. Find the sides of a square.

\newline

100\text{cm}

\newline

50\text{cm}

\newline

98\text{cm}

Find Circumference: First, we need to find the circumference of the original circle, which will be equal to the perimeter of the square since the wire is bent to form the square. The formula for the circumference of a circle is $C = 2\pi r$ , where $r$ is the radius of the circle.
Calculate Circumference: We know the radius $r = 49$ cm. Let's use $\pi \approx 3.14$ to calculate the circumference. $\newline$ Circumference $C = 2 \times 3.14 \times 49$ cm.
Calculate Side Length: Now, let's perform the calculation: $\newline$ Circumference $C = 2 \times 3.14 \times 49$ cm $= 307.72$ cm.
Find Side Length: The circumference of the circle, which is now the perimeter of the square, is $307.72\,\text{cm}$ . Since the perimeter of a square is the sum of all its four sides, we can find the length of one side by dividing the perimeter by $4$ .
Find Side Length: The circumference of the circle, which is now the perimeter of the square, is $307$ . $72$ cm. Since the perimeter of a square is the sum of all its four sides, we can find the length of one side by dividing the perimeter by $4$ .Let's calculate the length of one side of the square: $\newline$ Side length $s = \frac{307.72 \text{ cm}}{4}$ .
Find Side Length: The circumference of the circle, which is now the perimeter of the square, is $307$ . $72$ cm. Since the perimeter of a square is the sum of all its four sides, we can find the length of one side by dividing the perimeter by $4$ .Let's calculate the length of one side of the square: $\newline$ Side length $s = \frac{307.72 \text{ cm}}{4}$ .Performing the division gives us: $\newline$ Side length $s = 76.93$ cm.

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