Class 7 Maths Chapter 11 Perimeter And Area Exercise 11.3 pdf notes:-
- Exercise 11.1
- Exercise 11.2
- Exercise 11.4`
Exercise 11.3 Class 7 maths Chapter 11 Pdf Notes:-
Ncert Solution for Class 7 Maths Chapter 11 Area And Perimeter Exercise 11.3 Tips:
A racing track is semi-circular at both ends (Fig 11.27).
Can you find the distance covered by an athlete if he takes two rounds
of a racing track? We need to find a method to find the distances around
when a shape is circular.
Circumference of a Circle
Tanya cut different cards, in curved shape from a cardboard. She wants to put lace around Base Height Area of Triangle
15 cm _ 87 cm 31.4 mm 1256 mm 22 cm __ 170.5 cm to decorate these cards. What length of the lace does she require for each? You cannot measure the curves with the help of a ruler, as these figures are not “straight”.
What can you do?
Here is a way to find the length of lace required for shape in Fig 11.28(a). Mark a
point on the edge of the card and place the card on the table. Mark the position of the
point on the table also
Now roll the circular card on the table along a straight line till
the marked point again touches the table. Measure the distance
along the line. This is the length of the lace required
. It is also the distance along the edge of the card
from the marked point back to the marked point.
You can also find the distance by putting a string on the edge
of the circular object and taking all round it.
The distance around a circular region is known as its circumference.
Do This Take a bottle cap, a bangle or any other circular object and find the circumference.
Now, can you find the distance covered by the athlete on the track by this method?
Still, it will be very difficult to find the distance around the track or any other circular
object by measuring through string. Moreover, the measurement will not be accurate.
So, we need some formula for this, as we have for rectilinear figures or shapes.
Let us see if there is any relationship between the diameter and the circumference of
Do This Take one each of quarter plate and half plate. Roll once each of these on
a table-top. Which plate covers more distance in one complete revolution?
Which plate will take less number of revolutions to cover the length of the
Area of Circle
Consider the following:
A farmer dug a flower bed of radius 7 m at the centre of a field. He needs to
purchase fertiliser. If 1 kg of fertiliser is required for 1 square metre area,
how much fertiliser should he purchase?
What will be the cost of polishing a circular table-top of radius 2 m at the rate
of 10 per square metre?
Can you tell what we need to find in such cases, Area or Perimeter? In such
cases we need to find the area of the circular region. Let us find the area of a circle, using
Draw a circle of radius 4 cm on a graph paper Find the area by counting
the number of squares enclosed.
As the edges are not straight, we get a rough estimate of the area of circle by this method.
There is another way of finding the area of a circle.
Draw a circle and shade one half of the circle Now fold the circle into
eighths and cut along the folds Arrange the separate pieces as shown,which is roughly a parallelogram.
The more sectors we have, the nearer we reach an appropriate parallelogram. As done above if we divide the circle in 64 sectors, and arrange these sectors. It
gives nearly a rectangle What is the breadth of this rectangle? The breadth of this rectangle is the radius of the
circle, i.e., ‘r’.
As the whole circle is divided into 64 sectors and on each side we have 32 sectors, the
length of the rectangle is the length of the 32 sectors, which is half of the circumference.
Area of the circle = Area of rectangle thus formed = l × b
= (Half of circumference) × radius = 1/2 X 2πrXr = πr2 So, the area of the circle = πr2
Try These Draw circles of different radii on a graph paper. Find the area by counting the
number of squares. Also find the area by using the formula. Compare the two answers.