How to Find the Radius of a Circle with a Given Circumference

Understanding the relationship between the circumference and the radius of a circle is a fundamental concept in geometry. In this article, we will explore the process of finding the radius of a circle when the circumference is given.

Introduction to Circumference and Radius

Before diving into the calculation, it's important to understand the terms involved:

Circumference: The distance around the edge of a circle. Radius: The distance from the center of the circle to any point on its edge.

The relationship between the circumference C and the radius r of a circle is given by the formula:

[ C 2pi r ]

Step-by-Step Guide to Calculate the Radius

Using 2πr Formula

To find the radius, r, when the circumference, C, is given, we start with the equation:

[ 2pi r C ]

We are given the circumference as 88 cm. Thus, the equation becomes:

[ 2pi r 88 ]

To isolate r, divide both sides by (2pi):

[ r frac{88}{2pi} ]

Using the approximation (pi approx 3.14):

[ r approx frac{88}{2 times 3.14} approx frac{88}{6.28} approx 14.01 , text{cm} ]

Alternative Methods

There are several ways to approach this problem, as demonstrated by various solutions. Here are a few additional methods:

Method 1: Simplified Proportional Calculation

Using the simplified form of the circumference formula:

[ 2pi r 88 ]

Simplifying by dividing both sides by 2:

[ pi r frac{88}{2} 44 ]

Finally, divide both sides by (pi):

[ r frac{44}{pi} approx frac{44}{3.14} approx 14 , text{cm} ]

Method 2: Direct Formula Application

Using the direct formula:

[ r frac{C}{2pi} ]

Substituting the given value of C:

[ r frac{88}{2pi} approx frac{88}{6.28} approx 14 , text{cm} ]

Method 3: Simplified Arithmetic Calculation

Using the simplified form of the circumference to radius calculation:

[ C 2pi r Rightarrow r frac{C}{2pi} ]

Substituting the given circumference:

[ r frac{88}{2pi} approx frac{88}{6.28} approx 14 , text{cm} ]

Conclusion

In summary, the radius of the circle with a circumference of 88 cm is approximately 14 cm. This calculation can be performed using various methods, but the most straightforward approach involves isolating the variable in the circumference formula.

Additional Resources

About Circumference Circle Math Is Fun Circumference of a Circle

For more in-depth learning and practice on this topic, explore the resources provided. Happy learning!