A wire is looped in the form of a circle of radius 14 cm. The same wire is bent into a square form. What must be the length of the side of the square?

To solve this problem, we start by determining the length of the wire. The wire is initially looped in the form of a circle with a radius of 14 cm. The circumference of the circle (which is the length of the wire) can be calculated using the formula:

\[
C = 2 \pi r
\]

where \( r = 14 \) cm.

\[
C = 2 \times 3.1416 \times 14 \text{ cm} \approx 87.92 \text{ cm}
\]

Now, the wire is bent into the form of a square. The length of the wire remains the same, so the perimeter of the square is equal to the circumference of the circle:

\[
\text{Perimeter of square} = 87.92 \text{ cm}
\]

Let \( s \) be the length of the side of the square. The perimeter of the square is given by:

\[
\text{Perimeter of square} = 4s
\]

So,

\[
4s = 87.92 \text{ cm}
\]

\[
s = \frac{87.92 \text{ cm}}{4} \approx 21.98 \text{ cm}
\]

Thus, the length of the side of the square is approximately **21.98 cm**.

Would you like more details or have any questions?

---

Here are 5 related questions to consider:
1. How would the side length of the square change if the radius of the circle were doubled?
2. What is the area of the square formed by the wire?
3. How does the area of the square compare to the area of the original circle?
4. If the wire was bent into the shape of an equilateral triangle instead, what would be the side length?
5. What is the relationship between the perimeter and the area of a square?

**Tip:** Remember, the perimeter of any shape formed by the wire will always be equal to the original length of the wire.

Learn how to calculate the side length of a square formed by bending a wire initially looped as a circle with a radius of 14 cm. Understand the application of circumference and perimeter formulas. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation