A wire is looped in the form of a circle of radius 28cm. It is re-bent into a square form. Find the length of the side of the square. [Use π = 22/7]
Explanation
To solve this problem, follow these steps:
1. Calculate the circumference of the circle:
The circumference \( C \) of a circle is given by:
\[
C = 2\pi r
\]
where \( r \) is the radius of the circle. Given \( r = 28 \) cm and \( \pi = \frac{22}{7} \), we can calculate:
\[
C = 2 \times \frac{22}{7} \times 28
\]
\[
C = \frac{44 \times 28}{7}
\]
\[
C = \frac{1232}{7} = 176 \text{ cm}
\]
2. Find the length of the wire used for the square:
When the wire is re-bent into a square, the length of the wire will be the perimeter of the square. Therefore, the perimeter of the square is also 176 cm.
3. Calculate the side length of the square:
The perimeter \( P \) of a square is given by:
\[
P = 4 \times \text{side length}
\]
Let \( s \) be the side length of the square. We can solve for \( s \):
\[
4s = 176
\]
\[
s = \frac{176}{4} = 44 \text{ cm}
\]
The length of the side of the square is 44 cm.
The correct answer is A. 44 cm.