The Area Of The Circular Field Is 154sq.m.find It Circumference Of The Field​

by ADMIN 78 views

Introduction

In mathematics, particularly in geometry, the area and circumference of a circle are two fundamental concepts that are often used to describe the size and shape of a circular field. The area of a circle is the amount of space inside the circle, while the circumference is the distance around the circle. In this article, we will explore the relationship between the area and circumference of a circular field and use this relationship to find the circumference of a circular field with an area of 154 sq.m.

The Formula for the Area of a Circle

The area of a circle is given by the formula:

A = πr^2

where A is the area of the circle, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

The Formula for the Circumference of a Circle

The circumference of a circle is given by the formula:

C = 2πr

where C is the circumference of the circle, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

Finding the Radius of the Circular Field

Given that the area of the circular field is 154 sq.m, we can use the formula for the area of a circle to find the radius of the field.

A = πr^2

Substituting the given value of the area, we get:

154 = πr^2

To find the value of r, we can divide both sides of the equation by π:

r^2 = 154/π

r^2 = 154/3.14

r^2 = 49.36

Taking the square root of both sides of the equation, we get:

r = √49.36

r = 7

Therefore, the radius of the circular field is 7 meters.

Finding the Circumference of the Circular Field

Now that we have found the radius of the circular field, we can use the formula for the circumference of a circle to find the circumference of the field.

C = 2πr

Substituting the value of r, we get:

C = 2π(7)

C = 2(3.14)(7)

C = 44.12

Therefore, the circumference of the circular field is approximately 44.12 meters.

Conclusion

In this article, we have explored the relationship between the area and circumference of a circular field and used this relationship to find the circumference of a circular field with an area of 154 sq.m. We have used the formulas for the area and circumference of a circle to find the radius of the field and then used the radius to find the circumference of the field. The result shows that the circumference of the circular field is approximately 44.12 meters.

Frequently Asked Questions

  • What is the formula for the area of a circle? The formula for the area of a circle is A = πr^2.
  • What is the formula for the circumference of a circle? The formula for the circumference of a circle is C = 2πr.
  • How do I find the radius of a circular field given its area? To find the radius of a circular field given its area, you can use the formula A = πr^2 and solve for r.
  • How do I find the circumference of a circular field given its radius? To find the circumference of a circular field given its radius, you can use the formula C = 2πr.

References

Introduction

In our previous article, we explored the relationship between the area and circumference of a circular field and used this relationship to find the circumference of a circular field with an area of 154 sq.m. In this article, we will answer some frequently asked questions related to the area and circumference of a circular field.

Q&A

Q: What is the formula for the area of a circle?

A: The formula for the area of a circle is A = πr^2, where A is the area of the circle, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

Q: What is the formula for the circumference of a circle?

A: The formula for the circumference of a circle is C = 2πr, where C is the circumference of the circle, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

Q: How do I find the radius of a circular field given its area?

A: To find the radius of a circular field given its area, you can use the formula A = πr^2 and solve for r. For example, if the area of the circular field is 154 sq.m, you can substitute this value into the formula and solve for r.

Q: How do I find the circumference of a circular field given its radius?

A: To find the circumference of a circular field given its radius, you can use the formula C = 2πr. For example, if the radius of the circular field is 7 meters, you can substitute this value into the formula and solve for C.

Q: What is the relationship between the area and circumference of a circular field?

A: The area and circumference of a circular field are related by the formulas A = πr^2 and C = 2πr. These formulas show that the area of a circular field is proportional to the square of its radius, while the circumference of a circular field is proportional to its radius.

Q: Can I use the formulas for the area and circumference of a circle to find the diameter of a circular field?

A: Yes, you can use the formulas for the area and circumference of a circle to find the diameter of a circular field. The diameter of a circular field is twice its radius, so if you know the radius of the field, you can find its diameter by multiplying the radius by 2.

Q: What is the significance of the mathematical constant π (pi) in the formulas for the area and circumference of a circle?

A: The mathematical constant π (pi) is a fundamental constant in mathematics that is approximately equal to 3.14. It is used in the formulas for the area and circumference of a circle to relate the area and circumference of a circle to its radius.

Q: Can I use the formulas for the area and circumference of a circle to find the area and circumference of a circular field with a diameter of 14 meters?

A: Yes, you can use the formulas for the area and circumference of a circle to find the area and circumference of a circular field with a diameter of 14 meters. First, find the radius of the field by dividing the diameter by 2. Then, use the formulas for the area and circumference of a circle to find the area and circumference of the field.

Conclusion

In this article, we have answered some frequently asked questions related to the area and circumference of a circular field. We have used the formulas for the area and circumference of a circle to find the radius and circumference of a circular field with an area of 154 sq.m, and we have explained the significance of the mathematical constant π (pi) in the formulas for the area and circumference of a circle.

Frequently Asked Questions

  • What is the formula for the area of a circle? The formula for the area of a circle is A = πr^2.
  • What is the formula for the circumference of a circle? The formula for the circumference of a circle is C = 2πr.
  • How do I find the radius of a circular field given its area? To find the radius of a circular field given its area, you can use the formula A = πr^2 and solve for r.
  • How do I find the circumference of a circular field given its radius? To find the circumference of a circular field given its radius, you can use the formula C = 2πr.

References