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

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Circles: word problems

Full solution

Q.

\newline

A man has bent a circular wire of radius

49\text{cm}

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

\newline

A)100\text{cm}

\newline

B)50\text{cm}

\newline

C)98\text{cm}

Calculate Circumference: First, we need to find the circumference of the original circle, which is the total length of the wire. The formula for the circumference $C$ of a circle is $C = 2\pi r$ , where $r$ is the radius.
Calculate Perimeter: We know the radius $r$ is $49$ cm, and we will use $\pi \approx 3.14$ for our calculations. So, the circumference $C = 2 \times 3.14 \times 49$ cm.
Find Side Length: Now, let's calculate the circumference: $C = 2 \times 3.14 \times 49 \, \text{cm} = 307.72 \, \text{cm}$ . This is the total length of the wire.
Find Side Length: Now, let's calculate the circumference: $C = 2 \times 3.14 \times 49 \, \text{cm} = 307.72 \, \text{cm}$ . This is the total length of the wire.Since the wire is bent to form a square, the circumference of the circle is equal to the perimeter of the square. The perimeter $(P)$ of a square is $P = 4 \times \text{side\_length}$ .
Find Side Length: Now, let's calculate the circumference: $C = 2 \times 3.14 \times 49 \, \text{cm} = 307.72 \, \text{cm}$ . This is the total length of the wire.Since the wire is bent to form a square, the circumference of the circle is equal to the perimeter of the square. The perimeter $(P)$ of a square is $P = 4 \times \text{side\_length}$ .To find the length of one side of the square, we divide the total length of the wire (which is the perimeter of the square) by $4$ . So, $\text{side\_length} = 307.72 \, \text{cm} / 4$ .
Find Side Length: Now, let's calculate the circumference: $C = 2 \times 3.14 \times 49 \, \text{cm} = 307.72 \, \text{cm}$ . This is the total length of the wire.Since the wire is bent to form a square, the circumference of the circle is equal to the perimeter of the square. The perimeter $(P)$ of a square is $P = 4 \times \text{side\_length}$ .To find the length of one side of the square, we divide the total length of the wire (which is the perimeter of the square) by $4$ . So, $\text{side\_length} = 307.72 \, \text{cm} / 4$ .Calculating the side length gives us: $\text{side\_length} = 307.72 \, \text{cm} / 4 = 76.93 \, \text{cm}$ . This is the length of each side of the square.

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