Calculating the Radius of a Circle from its Circumference

When trying to find the radius of a circle, a fundamental step in geometry, we often use the circle's circumference. The relationship between the circumference and the radius is clearly defined through the formula C 2πr. In this article, we will explore how to find the radius of a circle given its circumference. Let's go through the process with a specific example where the circumference is 22 cm.

Understanding the Formula

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

C 2πr

Here: C is the circumference of the circle. r is the radius of the circle. π (pi) is a mathematical constant approximately equal to 3.1416.

Example: Finding the Radius Given a Circumference

Suppose we have a circle with a circumference of 22 cm. Our goal is to determine the radius of the circle. We can use the formula C 2πr to do this. Rearranging the formula, we can solve for the radius (r):

r C / 2π

Substituting the given value of the circumference (C 22 cm) into the formula, we get:

r 22 / (2 × 3.1416)

Calculating the right-hand side, we have:

r ≈ 22 / 6.2832 ≈ 3.501 cm

Therefore, the radius of the circle is approximately 3.5 cm.

Key Calculations for Clarity

For better clarity and to ensure accuracy, we can break down the calculations step-by-step:

Given:

Circumference (C) 22 cm

Using the formula:

C 2πr

22 2πr

Divide both sides by 2π:

r 22 / 2π

Calculating:

r 22 / (2 × 3.1416) ≈ 22 / 6.2832 ≈ 3.501 cm

Conclusion

The radius of a circle can be calculated from its circumference using the formula r C / 2π. In this example, we found that a circle with a circumference of 22 cm has a radius of approximately 3.5 cm. Understanding this relationship is crucial not only for basic geometry but also for more advanced applications in mathematics and other sciences.

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