Performing the Calculation

Oct 13, 2025 by windailys.com 38 views

Introduction

In mathematics, the relationship between the circumference and the radius of a circle is a fundamental concept that has been studied for centuries. The circumference of a circle is the distance around the circle, while the radius is the distance from the center of the circle to the edge. In this article, we will explore how to find the radius of a circle given its circumference, using the approximation of pi (π) as 3.14.

The Formula: Circumference = 2πr

The formula for the circumference of a circle is given by:

C = 2πr

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

Given the Circumference, Find the Radius

We are given that the circumference of the circle is 125.6 kilometers. We can use the formula C = 2πr to find the radius of the circle.

First, we need to rearrange the formula to isolate the radius (r):

r = C / (2π)

Now, we can plug in the value of the circumference (C = 125.6 km) and the value of π (π ≈ 3.14) into the formula:

r = 125.6 km / (2 × 3.14)

Performing the Calculation

To find the radius, we need to perform the calculation:

r = 125.6 km / (2 × 3.14) = 125.6 km / 6.28 = 20.0 km

Rounding the Answer to the Nearest Hundredth

We are asked to round our answer to the nearest hundredth. Since the radius is 20.0 km, which is already a whole number, we do not need to round it.

Conclusion

In conclusion, we have used the formula C = 2πr to find the radius of a circle given its circumference. By rearranging the formula to isolate the radius, we were able to plug in the values of the circumference and π to find the radius. The radius of the circle is 20.0 km, rounded to the nearest hundredth.

Additional Tips and Tricks

Make sure to use the correct value of π (π ≈ 3.14) when performing calculations involving the circumference and radius of a circle.
When rearranging the formula to isolate the radius, make sure to multiply both sides of the equation by the reciprocal of the coefficient of the radius (in this case, 1/2π).
When performing calculations involving the circumference and radius of a circle, make sure to use the correct units (e.g., kilometers, meters, etc.).

Real-World Applications

The relationship between the circumference and the radius of a circle has many real-world applications, including:

Engineering: When designing circular structures, such as bridges or tunnels, engineers need to calculate the radius of the circle to ensure that it is strong enough to support the weight of the structure.
Architecture: Architects use the relationship between the circumference and the radius of a circle to design circular buildings, such as domes or spheres.
Physics: Physicists use the relationship between the circumference and the radius of a circle to study the properties of circular motion and the behavior of objects in circular orbits.

Common Mistakes to Avoid

Using the wrong value of π: Make sure to use the correct value of π (π ≈ 3.14) when performing calculations involving the circumference and radius of a circle.
Rounding the answer incorrectly: Make sure to round the answer to the nearest hundredth, as specified in the problem.
Not using the correct units: Make sure to use the correct units (e.g., kilometers, meters, etc.) when performing calculations involving the circumference and radius of a circle.

Conclusion

In conclusion, the relationship between the circumference and the radius of a circle is a fundamental concept in mathematics that has many real-world applications. By using the formula C = 2πr and rearranging it to isolate the radius, we can find the radius of a circle given its circumference. Remember to use the correct value of π, round the answer to the nearest hundredth, and use the correct units when performing calculations involving the circumference and radius of a circle.