Measurement: Circumference of Circle


The perimeter of a circle is known as its circumference.

circumference of circle


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.

ObjectDiameterCircumference
CD12 cm38 cm
Bottle lid9 cm28 cm
Frisbee20 cm63 cm
Bowl7 cm22 cm
Key ring2 cm6 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
7
  times its diameter.
The value  22
7
  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.
find circumference

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.
find circumference

Radius  =  21 cm
Circumference  =  2 × π × 21 cm
   =  2 × 22
71
 × 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.

find perimeter of semicircle
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.

find perimeter of quadrant

Perimeter of a quadrant  =  A quarter of the circumference of circle
  + (2 × radius)
   =  (1
42
× 21 × 3.14 × 5) + (2 × 5)
   =  7.85  +  10
   =  17.85 cm

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

find perimeter of three-quarter circle

Perimeter of 3
4
 circle  =  3
4
 of the circumference of the circle
    + (2 × radius)
     =  (3
421
× 21 ×2211
71
× 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.

find distance travelled

Spoke of the wheel  =  Radius of the wheel
1 rotation of the wheel  =  Circumference of the wheel
   =  
2 × 22
71
× 355 cm
   =  220 cm
   =  2.2 m

The wheel travels 2.2 m in 1 rotation.