● To understand the concepts
of area and circumference of circle.
● To understand the area
of circular and rectangular pathways.
We have already studied that closed shapes
such as rectangle and square having area and perimeter. Pasting of tiles on a wall,
paving a parking lot with stones, fencing a field or ground etc., are some of the
places where the knowledge of area and perimeter of rectangle are essential. In
this chapter, we extend this concept to circles. The best example of a circle is
the wheel. The invention of wheel is perhaps the greatest achievement of mankind.
The teacher shows the following pictures
of wheel and asks questions as given below:
Teacher : Bharath, can
you tell me what is the name of the picture given in Fig 2.1?
Bharath : Yes Sir/Madam,
wheel of a bicycle.
Teacher : Sathish, would
you tell me what is in Fig.2.2?
Sathish : Yes Sir/Madam,
it is a wheel of a car.
Teacher : Suresh, will
you name the shape of both figures?
Suresh : Yes Sir/Madam,
they are circular in shape.
Teacher : Yes, you are
right. Now Mary, will you tell me the distance covered by the wheel when it rotates
Mary : I don’t know sir/madam.
Teacher : Ok, How do we
measure the distance around the circle? We cannot measure the curves with the help
of a ruler, as these shapes do not have straight edges. But there is a way to measure
the distance around the circle. Mark a point on its boundary. Place the wheel on the floor in such
a way that the marked point coincides with the floor. Take it as the initial point.
Rotate the wheel once on the floor along a straight line till the marked point again
touches the floor. The distance covered by
it is the distance around the outer edge
of a circle. That is, Circumference
Suresh :Teacher, is there
any other way to find the distance?
Teacher : Yes, mark a point
on its boundary and using a thread and scale we can measure its length.
We are now going to discuss
the circumference and area of the circle.
MATHEMATICS ALIVE - Measurements in Real Life