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Topics: Circle
A man has bent a circular wire of radius
49cm to form a square. Find the sides of a square.

100cm

50cm

Topics: Circle $\newline$ A man has bent a circular wire of radius $49 \mathrm{~cm}$ to form a square. Find the sides of a square. $\newline$ $100 \mathrm{~cm}$ $\newline$ $50 \mathrm{~cm}$

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Circles: word problems

Full solution

Q. Topics: Circle

\newline

A man has bent a circular wire of radius

49 \mathrm{~cm}

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

\newline

100 \mathrm{~cm}

\newline

50 \mathrm{~cm}

Find Circumference of Circle: First, we need to find the circumference of the original circle, which is the length of the wire before it was bent into a square shape. The formula for the circumference of a circle is $C = 2\pi r$ , where $r$ is the radius.
Calculate Circumference: We know the radius $r = 49$ cm. Let's plug this value into the formula to find the circumference. $\newline$ So, $C = 2 \times \pi \times 49$ . $\newline$ We can use $\pi \approx 3.14$ for our calculations.
Find Perimeter of Square: Now, let's calculate the circumference. $\newline$ $C = 2 \times 3.14 \times 49$ cm. $\newline$ $C = 6.28 \times 49$ cm. $\newline$ $C = 307.72$ cm. $\newline$ This is the total length of the wire.
Calculate Side Length: Since the wire is bent into a square, all four sides of the square will be of equal length. Let's call the length of each side of the square $s$ . $\newline$ The perimeter of a square is given by $P = 4s$ .
Round to Nearest Whole Number: We know the perimeter of the square is equal to the circumference of the circle, which is the length of the wire. Therefore, $4s = 307.72$ cm.
Round to Nearest Whole Number: We know the perimeter of the square is equal to the circumference of the circle, which is the length of the wire. Therefore, $4s = 307.72$ cm.To find the length of one side of the square, we divide the total length of the wire by $4$ . $\newline$ $s = \frac{307.72}{4}$ cm. $\newline$ $s = 76.93$ cm.
Round to Nearest Whole Number: We know the perimeter of the square is equal to the circumference of the circle, which is the length of the wire. Therefore, $4s = 307.72$ cm.To find the length of one side of the square, we divide the total length of the wire by $4$ . $\newline$ $s = \frac{307.72}{4}$ cm. $\newline$ $s = 76.93$ cm.We round the length of one side of the square to the nearest whole number, if necessary. However, in this case, we can leave it as $s = 76.93$ cm since the problem does not specify rounding to the nearest whole number.

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