A Piece Of Wire Is Bunt In A Square Of Area 144 Cm^2 If Some Wore Is Bent In A Circle ,find Its Radius​

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Introduction

In this article, we will explore the relationship between the area of a square and the radius of a circle when a piece of wire is bent to form both shapes. We will use the given area of the square to find the length of the wire, and then use this length to determine the radius of the circle.

The Area of a Square

A square is a quadrilateral with four equal sides and four right angles. The area of a square is given by the formula:

Area = side^2

where side is the length of one side of the square. In this case, the area of the square is given as 144 cm^2.

Finding the Length of the Wire

To find the length of the wire, we need to find the perimeter of the square. The perimeter of a square is given by the formula:

Perimeter = 4 * side

Since the area of the square is 144 cm^2, we can find the length of one side by taking the square root of the area:

side = √144 = 12 cm

Now, we can find the perimeter of the square:

Perimeter = 4 * 12 = 48 cm

Since the wire is bent to form the square, the length of the wire is equal to the perimeter of the square:

Length of wire = 48 cm

The Length of the Wire as the Circumference of a Circle

When the wire is bent to form a circle, the length of the wire becomes the circumference of the circle. The circumference of a circle is given by the formula:

Circumference = 2 * π * radius

where radius is the radius of the circle. We can set up an equation using the length of the wire as the circumference:

48 = 2 * π * radius

Solving for the Radius

To solve for the radius, we can divide both sides of the equation by 2 * π:

radius = 48 / (2 * π)

radius = 48 / (2 * 3.14159)

radius = 48 / 6.28318

radius = 7.643

Conclusion

In this article, we used the area of a square to find the length of the wire, and then used this length to determine the radius of a circle. We found that the radius of the circle is approximately 7.643 cm.

Key Takeaways

  • The area of a square is given by the formula: Area = side^2
  • The perimeter of a square is given by the formula: Perimeter = 4 * side
  • The length of the wire is equal to the perimeter of the square
  • The circumference of a circle is given by the formula: Circumference = 2 * π * radius
  • The radius of a circle can be found by dividing the circumference by 2 * π

Further Reading

If you want to learn more about the relationship between the area of a square and the radius of a circle, you can check out the following resources:

References

Introduction

In our previous article, we explored the relationship between the area of a square and the radius of a circle when a piece of wire is bent to form both shapes. We used the given area of the square to find the length of the wire, and then used this length to determine the radius of the circle. In this article, we will answer some frequently asked questions related to this topic.

Q: What is the relationship between the area of a square and the radius of a circle?

A: The area of a square is given by the formula: Area = side^2, where side is the length of one side of the square. The circumference of a circle is given by the formula: Circumference = 2 * π * radius, where radius is the radius of the circle. When a piece of wire is bent to form a square and then a circle, the length of the wire is equal to the perimeter of the square and the circumference of the circle.

Q: How do I find the length of the wire when it is bent to form a square?

A: To find the length of the wire, you need to find the perimeter of the square. The perimeter of a square is given by the formula: Perimeter = 4 * side, where side is the length of one side of the square. Since the area of the square is given, you can find the length of one side by taking the square root of the area: side = √Area.

Q: How do I find the radius of a circle when the length of the wire is known?

A: To find the radius of a circle, you can use the formula: Circumference = 2 * π * radius, where circumference is the length of the wire. You can rearrange this formula to solve for the radius: radius = Circumference / (2 * π).

Q: What is the significance of the value of π in the formula for the circumference of a circle?

A: The value of π is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is approximately equal to 3.14159. The value of π is used in the formula for the circumference of a circle to ensure that the circumference is calculated accurately.

Q: Can I use this method to find the radius of a circle when the area of a rectangle is given?

A: No, this method is specific to finding the radius of a circle when the area of a square is given. If you are given the area of a rectangle, you will need to use a different method to find the radius of the circle.

Q: What are some real-world applications of this concept?

A: This concept has many real-world applications, such as:

  • Engineering: When designing a circular structure, such as a bridge or a tunnel, engineers need to calculate the radius of the circle to ensure that it is strong and stable.
  • Architecture: Architects use this concept to design circular buildings and structures, such as domes and arches.
  • Physics: Physicists use this concept to calculate the circumference of a circle when studying the motion of objects in circular paths.

Q: Can I use a calculator to find the radius of a circle when the length of the wire is known?

A: Yes, you can use a calculator to find the radius of a circle when the length of the wire is known. Simply enter the length of the wire and the value of π into the calculator, and it will give you the radius of the circle.

Conclusion

In this article, we have answered some frequently asked questions related to the relationship between the area of a square and the radius of a circle when a piece of wire is bent to form both shapes. We hope that this article has been helpful in clarifying any doubts you may have had about this concept.

Key Takeaways

  • The area of a square is given by the formula: Area = side^2
  • The perimeter of a square is given by the formula: Perimeter = 4 * side
  • The circumference of a circle is given by the formula: Circumference = 2 * π * radius
  • The radius of a circle can be found by dividing the circumference by 2 * π
  • The value of π is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Further Reading

If you want to learn more about the relationship between the area of a square and the radius of a circle, you can check out the following resources:

References