Calculating the Diameter of a Circle Given Its Circumference

Introduction: The relationship between the circumference of a circle and its diameter is a fundamental concept in geometry. This article will walk you through the steps to calculate the diameter of a circle when given its circumference, using the value of (pi) as (frac{22}{7}). This knowledge is crucial for many real-world applications and is often a key topic in educational curricula.

Understanding the Formula

The circumference of a circle, denoted as (C), is given by the formula:

[C 2pi r]

Where:

(r) is the radius of the circle, (pi) is a constant approximately equal to 3.14159.

Using the Given Circumference

In the problem statement, we are given the circumference, (C 44) meters. Let's calculate the diameter, denoted as (D), using this value.

Step-by-Step Calculation

Start with the formula for circumference:

[C 2pi r]

Rearrange the formula to solve for the radius (r):

[r frac{C}{2pi}]

Substitute the given value of circumference into the formula:

[r frac{44}{2 times frac{22}{7}} frac{44 times 7}{22 times 2} frac{44}{2 times 22} times 7 frac{44}{44} times 7 7]

So, the radius of the circle is 7 meters.

Calculating the Diameter

Now, to find the diameter, use the formula:

[D 2r]

Substitute the calculated radius:

[D 2 times 7 14]

Alternative Methods

There are several other methods to solve this problem, each with its own unique approach:

Method 1: Using the Circumference-Diameter Relationship

Another way to find the diameter is to use the relationship between the circumference and diameter:

[C pi D]

Given that the circumference is 44 meters and using (pi frac{22}{7}):

[44 frac{22}{7} times D]

Solve for (D) by rearranging the formula:

[D frac{44 times 7}{22} frac{44 times 7}{22} 14]

Method 2: Directly Solving for the Diameter

A simpler way is to directly calculate the diameter from the circumference:

[D frac{C}{pi} frac{44}{frac{22}{7}} 14]

This confirms that the diameter of the circle is 14 meters.

Conclusion

By understanding the relationship between the circumference and the diameter of a circle, you can easily solve for either value. The methods described in this article provide clear and straightforward ways to calculate the diameter of a circle given its circumference. Whether you prefer algebraic manipulation or direct substitution, these strategies are widely used in geometry and practical applications.