## What is the Circumference of a Circle and How to Measure it?

#### What is the circumference of a circle?

The perimeter of a circle is known as its circumference.

Trace the outline of a few circular objects of different sizes like a CD, a circular bottle lid, a frisbee, a round bowl and a key ring on paper and cut them along their circumference. Then, do the following:

As you will notice, the circumference of each object is about 3 times its diameter.

More precisely, the circumference of a circle is

The value

is represented by

The approximate value of π is

Trace the outline of a few circular objects of different sizes like a CD, a circular bottle lid, a frisbee, a round bowl and a key ring on paper and cut them along their circumference. Then, do the following:

- Measure the diameter of each circle by folding in half.
- Measure the circumference of each circle using a string.
- Record both readings in a table as below.

As you will notice, the circumference of each object is about 3 times its diameter.

More precisely, the circumference of a circle is

**times its diameter.**

22 |

7 |

The value

22 |

7 |

**π**and read as**pi**.The approximate value of π is

**3.14**.#### What is the formula to calculate circumference of a circle?

Circumference = π × Diameter

Or,

Circumference = π × 2 × Radius = 2 × π × Radius

Or,

Circumference = π × 2 × Radius = 2 × π × Radius

#### 1. Find the circumference of the circles below.

a)

Diameter = 8 cm

Circumference = π × 8 cm = 3.14 × 8 cm =

Diameter = 8 cm

Circumference = π × 8 cm = 3.14 × 8 cm =

**25.12 cm**
b)

Radius = 21 cm

Circumference

= 2 × π × 21 cm

= 2 ×

× ~~21~~

=

Circumference

= 2 × π × 21 cm

= 2 ×

22 |

_{1}7 |

^{3}cm=

**132 cm**
When calculation is easy, we use

instead of 3.14 as the value of π

22 |

7 |

#### 2. Find the perimeters of the following figures.

Round off your answers to 2 decimal places.

a) A semicircle of diameter 17.6 cm.

Perimeter of a semicircle

= Half the circumference of the circle + diameter

= (

× π × 17.6) + 17.6

= (

× 3.14 × 17.6) + 17.6

= 27.632 + 17.6

= 45.232

≈ 45.23 cm

Perimeter of a semicircle

= Half the circumference of the circle + diameter

= (

1 |

2 |

= (

1 |

2 |

= 27.632 + 17.6

= 45.232

≈ 45.23 cm

b) A quadrant of radius 5 cm.

Perimeter of a quadrant

= A quarter of the circumference of circle + (2 × radius)

= (

× ~~2~~

= 7.85 + 10

= 17.85 cm

Perimeter of a quadrant

= A quarter of the circumference of circle + (2 × radius)

= (

1 |

_{2}4 |

^{1}× 3.14 × 5) + (2 × 5)= 7.85 + 10

= 17.85 cm

c) A three-quarter circle of radius 84 cm.

Perimeter of

circle

=

of the circumference of the circle + (2 × radius)

= (

× ~~2~~

× ~~84~~

= (

× 1 ×

× 12) + 168

= 396 + 168

= 564 cm

Perimeter of

3 |

4 |

=

3 |

4 |

= (

3 |

_{2}4 |

^{1}×22 |

_{1}7 |

^{12}) + (2 × 84)= (

3 |

_{1}2 |

22^{11} |

1 |

= 396 + 168

= 564 cm

#### 3. Can a pizza of radius 12 cm fit into a plate that has a circumference of 100 cm?

Circumference of pizza = 2 × 3.14 × 12 = 75.36 cm

75.36 cm < 100 cm

Yes, the pizza can fit into the plate.

75.36 cm < 100 cm

Yes, the pizza can fit into the plate.

#### 4. The spoke of a wheel is 35 cm long.

How far does the wheel travel in 1 rotation?

Give your answer in metres.

Spoke of the wheel = Radius of the wheel

1 rotation of the wheel

= Circumference of the wheel

= 2 ×

22 |

_{1}7 |

^{5}

= 220 cm

= 2.2 m

The wheel travels

**2.2 m**in 1 rotation.