# Measurement: Circumference of 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:

- 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.

ObjectDiameterCircumferenceCD 12 cm 38 cm Bottle lid 9 cm 28 cm Frisbee 20 cm 63 cm Bowl 7 cm 22 cm Key ring 2 cm 6 cm

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

More precisely, the circumference of a circle is 22

7times its diameter.

The value 22

7is represented by πand read aspi.Circumference = π × DiameterThe approximate value of π is

Or,

Circumference = π × 2 × Radius

= 2 × π × Radius3.14.

*Problem 1*

*Problem 1*

Find the circumference of the circles below.a.

Diameter = 8 cm Circumference = π × 8 cm = 3.14 × 8 cm = 25.12 cm

b.When calculation is easy, wethe value of π.

use 22

7instead of 3.14 as

Radius = 21 cm Circumference = 2 × π × 21 cm = 2 × 22~~7~~_{1}× ~~21~~^{3}cm= 132 cm

*Problem 2*

*Problem 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 = ( 1

2× π × 17.6) + 17.6 = ( 1

2× 3.14 × 17.6) + 17.6 = 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) = ( 1~~4~~_{2}× ~~2~~^{1}× 3.14 × 5) + (2 × 5)= 7.85 + 10 = 17.85 cm

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

Perimeter of 3

4circle = 3

4of the circumference of the circle + (2 × radius) = ( 3~~4~~_{21}× ~~2~~^{1}×~~22~~^{11}~~7~~_{1}× ~~84~~^{12}) + (2 × 84)= 396 + 168 = 564 cm

*Problem 3*

*Problem 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.

*Problem 4*

*Problem 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~~7~~_{1}× ~~35~~^{5}cm= 220 cm = 2.2 m

The wheel travels 2.2 m in 1 rotation.