Skill: Explore the relationship between circumference and diameter

The circumference is the distance around a circle. The diameter is the distance across the circle through its center.

For every circle, the ratio of circumference to diameter is approximately the same:

$$\frac{C}{d}\approx 3.14$$

This constant ratio is called $\pi$ (pi). Therefore, the formula is

$$C=\pi d$$

Worked example

A circular garden has a diameter of $8$ meters. Find its circumference.

Step 1: Identify the diameter.

$$d=8\text{ m}$$

Step 2: Use the formula.

$$C=\pi d$$

Step 3: Substitute $3.14$ for $\pi$ and $8$ for $d$.

$$C\approx 3.14(8)$$

Step 4: Calculate.

$$C\approx 25.12\text{ m}$$

The garden’s circumference is approximately

$$\boxed{25.12\text{ meters}}$$

This works because the circumference is always about $3.14$ times the diameter. For example, dividing the answer by the diameter gives

$$\frac{25.12}{8}=3.14$$

So, if the diameter becomes larger, the circumference becomes larger in the same proportion.