A Circumferance Of A Circle Is 146mm Calculate The Area Of The Circle To 1d.p

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Introduction

In mathematics, the circumference and area of a circle are two fundamental concepts that are closely related. The circumference of a circle is the distance around the circle, while the area is the space inside the circle. In this article, we will explore how to calculate the area of a circle given its circumference. We will use the formula for the area of a circle, which is A = πr^2, where A is the area and r is the radius of the circle.

Understanding the Relationship Between Circumference and Radius

The circumference of a circle is given by the formula C = 2Ï€r, where C is the circumference and r is the radius. To find the radius of the circle, we can rearrange this formula to solve for r: r = C / (2Ï€). In our problem, the circumference of the circle is given as 146mm. We can use this value to find the radius of the circle.

Calculating the Radius of the Circle

To calculate the radius of the circle, we can plug in the value of the circumference into the formula: r = C / (2Ï€). Substituting the value of C = 146mm, we get:

r = 146mm / (2Ï€)

Using the value of π as approximately 3.14, we can calculate the value of r:

r = 146mm / (2 x 3.14) r = 146mm / 6.28 r = 23.3mm

Calculating the Area of the Circle

Now that we have found the radius of the circle, we can use the formula A = πr^2 to calculate the area of the circle. Plugging in the value of r = 23.3mm, we get:

A = π(23.3mm)^2 A = 3.14 x 541.29mm^2 A = 1700.3mm^2

Rounding this value to 1 decimal place, we get:

A = 1700.3mm^2 ≈ 1700.3mm^2

Conclusion

In this article, we have shown how to calculate the area of a circle given its circumference. We used the formula for the area of a circle, A = πr^2, and the formula for the circumference of a circle, C = 2πr, to find the radius of the circle and then calculate the area. We found that the area of the circle is approximately 1700.3mm^2.

Formula Summary

  • Circumference of a circle: C = 2Ï€r
  • Area of a circle: A = Ï€r^2
  • Radius of a circle: r = C / (2Ï€)

Example Use Case

This formula can be used in a variety of real-world applications, such as:

  • Calculating the area of a circular room or building
  • Determining the size of a circular plot of land
  • Finding the area of a circular object, such as a coin or a wheel

Tips and Tricks

  • Make sure to use the correct value of Ï€, which is approximately 3.14.
  • Use a calculator to simplify calculations and avoid errors.
  • Double-check your calculations to ensure accuracy.

Further Reading

For more information on the circumference and area of a circle, see the following resources: