Circumference of a Circle

Learn to calculate the distance around a circle

1. What is Circumference?

Definition

The circumference is the distance around a circle. It is like the perimeter of a circle.

Visual: The Circumference

The circumference is the curved boundary of the circle

2. The Magic Number: Pi ( $\pi$ )

Discovery

When you divide the circumference of ANY circle by its diameter, you always get the same number. It starts 3.14159... and never ends.

$\frac{\text{Circumference}}{\text{Diameter}} \approx 3.14$

This special number is called pi (pronounced "pie") and is written as $\pi$ .

Values of Pi We Use

Decimal Form

$\pi = 3.14$

Fraction Form

$\pi = \frac{22}{7}$

Note: Always use the value of $\pi$ that the question gives. $\frac{22}{7}$ is usually given when the radius or diameter is a multiple of 7, because the 7 cancels.

3. The Circumference Formula

Two Forms of the Formula

When diameter is given:

C = $\pi$ × d

When radius is given:

C = 2 × $\pi$ × r

Remember: Since d = 2r, both formulas give the same answer!

4. Finding Circumference (Diameter Given)

Example 1: $(\text{Take } \pi = \frac{22}{7})$

A circle has a diameter of 21 cm. Find its circumference.

Solution:

Circumference = $\pi$ × Diameter

$= \frac{22}{7} \times 21$

= 66 cm

Example 2: $(\text{Take } \pi = 3.14)$

The diameter of a hula hoop is 70 cm. Find the circumference of the hoop.

Solution:

Circumference = $\pi$ × Diameter

= 3.14 × 70 cm

= 219.8 cm

5. Finding Circumference (Radius Given)

Two Methods

When the radius is given, you can either:

Method 1: Find the diameter first, then use C = $\pi$ × d
Method 2: Use the formula C = 2 × $\pi$ × r directly

Example 3: $(\text{Take } \pi = \frac{22}{7})$

The radius of a circle is 7 m. Find its circumference.

Method 1:

Diameter = 2 × 7 m = 14 m

C = $\pi$ × d

$= \frac{22}{7} \times 14$

= 44 m

Method 2:

C = 2 × $\pi$ × r

$= 2 \times \frac{22}{7} \times 7$

= 44 m

6. Practice Problems

Problem 1 $(\text{Take } \pi = \frac{22}{7})$

A circle has a diameter of 14 cm. Find its circumference.

ShowHide solution

C = $\pi$ × d

$= \frac{22}{7} \times 14$

= 44 cm

Problem 2 $(\text{Take } \pi = 3.14)$

The radius of a circle is 10 cm. Find its circumference.

ShowHide solution

C = 2 × $\pi$ × r

= 2 × 3.14 × 10

= 62.8 cm

Problem 3 $(\text{Take } \pi = \frac{22}{7})$

A circular track has a radius of 35 m. How far does an athlete run if they complete one lap?

ShowHide solution

C = 2 × $\pi$ × r

$= 2 \times \frac{22}{7} \times 35$

= 220 m

The athlete runs 220 m in one lap.

Problem 4 $(\text{Take } \pi = 3.14)$

A circular table has a diameter of 1.5 m. Find the circumference of the table.

ShowHide solution

C = $\pi$ × d

= 3.14 × 1.5

= 4.71 m

Key Takeaways

Circumference is the distance around a circle (like perimeter).

Pi ( $\pi$ ) ≈ 3.14 or $\frac{22}{7}$

Formula with diameter: C = $\pi$ × d

Formula with radius: C = 2 × $\pi$ × r

Use the value of π that the question gives. $\frac{22}{7}$ is usually given when the measurement is a multiple of 7, because the 7 cancels.

Circumference of a Circle

1. What is Circumference?

Definition

Visual: The Circumference

2. The Magic Number: Pi (π\piπ)

Discovery

Values of Pi We Use

3. The Circumference Formula

Two Forms of the Formula

4. Finding Circumference (Diameter Given)

Example 1: (Take π=227)(\text{Take } \pi = \frac{22}{7})(Take π=722​)

Example 2: (Take π=3.14)(\text{Take } \pi = 3.14)(Take π=3.14)

5. Finding Circumference (Radius Given)

Two Methods

Example 3: (Take π=227)(\text{Take } \pi = \frac{22}{7})(Take π=722​)

6. Practice Problems

Problem 1 (Take π=227)(\text{Take } \pi = \frac{22}{7})(Take π=722​)

Problem 2 (Take π=3.14)(\text{Take } \pi = 3.14)(Take π=3.14)

Problem 3 (Take π=227)(\text{Take } \pi = \frac{22}{7})(Take π=722​)

Problem 4 (Take π=3.14)(\text{Take } \pi = 3.14)(Take π=3.14)

Key Takeaways

2. The Magic Number: Pi ( $\pi$ )

Example 1: $(\text{Take } \pi = \frac{22}{7})$

Example 2: $(\text{Take } \pi = 3.14)$

Example 3: $(\text{Take } \pi = \frac{22}{7})$

Problem 1 $(\text{Take } \pi = \frac{22}{7})$

Problem 2 $(\text{Take } \pi = 3.14)$

Problem 3 $(\text{Take } \pi = \frac{22}{7})$

Problem 4 $(\text{Take } \pi = 3.14)$