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

 Object Diameter Circumference CD 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 227 times its diameter.
 The value 227 is represented by π and read as pi.
Circumference  =  π × Diameter
Or,
Circumference  =  π × 2 × Radius
=  2 × π × Radius
The approximate value of π is 3.14.

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, we
 use 22 7 instead of 3.14 as
the value of π.

 Radius = 21 cm Circumference = 2 × π × 21 cm = 2 × 2271 × 213 cm = 132 cm

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 = ( 12 × π × 17.6) + 17.6 = ( 12 × 3.14 × 17.6) + 17.6 = 27.632 + 17.6 = 45.232 ≈ 45.23 cm

 Perimeter of a quadrant = A quarter of the circumference of circle + (2 × radius) = ( 142 × 21 × 3.14 × 5) + (2 × 5) = 7.85  +  10 = 17.85 cm

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

 Perimeter of 34 circle = 34 of the circumference of the circle + (2 × radius) = ( 3421 × 21 × 221171 × 8412) + (2 × 84) = 396  +  168 = 564 cm

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

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 × 2271 × 355 cm
=  220 cm
=  2.2 m

The wheel travels 2.2 m in 1 rotation.