Explore the relationship between circumference and diameter

The circumference of any circle is proportional to its diameter: dividing circumference by diameter gives the constant ratio π, approximately 3.14 (or 22/7), so $C=\pi d$ . This relationship can be interpreted through measurements, tables, graphs, and formulas, and supports solving for circumference or diameter and understanding scale in circular measurement; formal proofs of π’s irrationality and more advanced derivations are not included.

Detailed Explanation: 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.

Learn by doing: Explore the relationship between circumference and diameter

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Circumference

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