Circumference of a Circle: Step-by-Step Examples

Hello there, math explorer! 👋 Understanding the circumference of a circle is a fundamental concept, and you're in the right place to get some clear, step-by-step examples. Let's dive in!

What is Circumference?

The circumference of a circle is simply the total distance around its edge. Think of it as the perimeter of a circular shape! 📏

The Formulas and Pi ($\pi$)

To calculate circumference ($C$), we use the mathematical constant Pi ($\pi$), approximately $3.14159$ or $\frac{22}{7}$. There are two primary formulas:

• Using the radius ($r$, the distance from the center to the edge): $C = 2\pi r$
• Using the diameter ($d$, the distance across the circle through the center; $d = 2r$): $C = \pi d$

Step-by-Step Examples!

Example 1: Given the Radius

Let's find the circumference of a circle with a radius of $7 \text{ cm}$.

1. Identify: Radius ($r$) is $7 \text{ cm}$.
2. Formula: Use $C = 2\pi r$.
3. Calculate: Substitute $r = 7$ and use $\pi \approx \frac{22}{7}$.
   $C = 2 \times \frac{22}{7} \times 7$
   $C = 2 \times 22$
   $C = 44 \text{ cm}$
   The circumference is $44 \text{ cm}$. Awesome! ✨

Example 2: Given the Diameter

Now, let's find the circumference of a circular object with a diameter of $10 \text{ inches}$.

1. Identify: Diameter ($d$) is $10 \text{ inches}$.
2. Formula: Use $C = \pi d$.
3. Calculate: Substitute $d = 10$ and use $\pi \approx 3.14$.
   $C = 3.14 \times 10$
   $C = 31.4 \text{ inches}$
   The circumference is approximately $31.4 \text{ inches}$. Easy peasy! 👍

Key Takeaways

Always remember:

• Circumference is the distance around a circle.
• $C = 2\pi r$ (with radius) or $C = \pi d$ (with diameter).
• $\pi$ is approximately $3.14$ or $\frac{22}{7}$.

Keep practicing these steps, and you'll master circumference in no time! Happy learning! 🚀