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we come across several circular shapes in our daily lives
this
is a pair of compasses
it is a tool to used to draw circular shapes
the distance between the pencil
and the sharp metallic tip is the radius
of the circle.
the radius of the circle we
just drew is thus 5 cm.
If you measure the distance between center of the circle
and any point on the circle
you will notice it is exactly 5 cm
We usually denote center of the circle as O
Let us now mark a point P on the circle
and measure OP
we see that OP
is equal to 5 cm
we say that OP
is a radius off the circle.
Radius is usually denoted
r
keep in mind that the plural of radius
is radii
let's now extend PO
to cut the circle at another point Q
we say that PQ
is the diameter
of the circle.
Note that the diameter
is a straight line
which divides the circle into two equal halves
and passes through its center.
We usually denote that diameter by d.
Do you notice
that the diameter is made up of
two radii?
Hence
diameter of a circle
is equal to twice it's radius
hence we write d
is equal to 2r.
let us now find the diameter of a pizza
which has a radius of 7 cm
We already learnt
that the diameter is twice the radius
therefore that diameter of the pizza
is 14 cm
Similarly if the diameter of a round table
is 100 cm
we can easily find its radius
by dividing the diameter by 2.
Radius
is equal to half
the diameter.
Therefore the radius of the table top is
50 cm.
The perimeter of the circle
is called
it's circumference
if you measure the
length of the circumference of any circle
and compare it with the diameter of the same circle
you will notice that it is about 3.14 its respective
diameter
this constant value is denoted by
pi.
The value of pi
is taken as 3.14
or 22 over 7
So if we know the diameter of a circle
we can easily find the circumference of that circle
by multiplying it by a 3.14 would fall
or 22 over 7
So remember
the formula to find a circumference of a circle
is pi times diameter
Let us find the circumference of a pizza
whose radius is 7 cm
taking the value of pi
as 22 over 7.
We know the circumference of a circle is pi times the diameter of the circle
or 22 over 7 times
the diameter of the circle.
We know the diameter
is 2 times radius.
Therefore
the circumference of the pizza
is pi times 2
times the radius
giving us the answer
44 cm
Now let us see how we can calculate the area
of a circle.
Let us imagine that we divide a circle
into 36 equal parts.
Notice that each portion of the circle almost resembles a isoceles
triangle
the height of which is equal to the radius of the circle.
We can now arrange the triangles
like this
We cut the last triangle into two equal portions
and place it in this way
and form a rectangle
The length of this rectangle
is equal to half
this circumference of the circle
while its breadth
is equal to the radius of the circle.
You already know that the circumference of a circle
is pi times diameter.
So we can say that half the circumference
is pi times radius.
You know we need to multiply the length and breadth of a rectangle
to find its area.
So in order to find the area of this rectangle,
we need to multiply the length and breadth
which could be written as
pi r squared.
Thus to find the area of a circle
we use the formula
pi r squared.
Let us find the area of the circle
whose radius is 14 cm.
Area
is equal to pi r squared.
22 over 7
times 14
times 14
is equal to
616
hence the area of the circle
is 616 square cm.