Area of Circle
Total surface on the plane covered by the
circumference of a circle is termed as the area
of circle. Area of circle is
given by the formula Area = πr2
where r is the radius of the circle. This formula can be understood and derived
by the following activities.
1. Take a circular shaped paper.
2. Cut the circle into two equal
halves.
3. Cut each half further into
small pieces equally as you can see in the figure.
4. Arrange the pieces of two halves in one place to form
like a rectangle as shown in the figure.
5. As we go on increasing the
number of small pieces it will tend to be a rectangle PQRS of length = half of
circumference (c/2) and breadth = radius (r).
We know, circumference of the circle (c)
= 2πr
∴ Length
of rectangle (l) = C/2 = 2πr/2 = πr
Breadth
of rectangle (b) = r
Now,
Area
of circle = Area of rectangle PQRS
=
length × breadth
=
πr × r
=
πr2
∴ Area of circle = πr2
Workout Examples
Example 1: Find the area of the circle having diameter of 14 cm.
Solution: Here,
Diameter (d) = 14 cm
∴ Radius (r) = d/2 = 14/2 = 7 cm
We
know,
Area
of circle = πr2
= 22/7 × 72
= 22/7 × 49
= 154 cm2
Example 2: Find the area of the circle whose circumference is 88 cm.
Solution: Here,
Circumference (C) = 88 cm
i.e. 2πr = 88
or, 2 × 22/7 × r = 88
or, 44/7 × r = 88
or, r = 88 × 7/44
or, r = 14 cm
We
know,
Area
of circle = πr2
= 22/7 × 142
= 22/7 × 196
= 616 cm2
Example 3: If the area of a circle is 154 cm2, then finds its
circumference.
Solution: Here,
Area of circle (A) = 154 cm2
i.e. πr2 = 154
or, 22/7 × r2 = 154
or, r2 = 154 × 7/22
or, r2 = 49
or, r2 = 72
or, r = 7 cm
Now,
Circumference of circle = 2πr
= 2 × 22/7 × 7
= 44 cm
Example 4: Find the area of the shaded region of the figure.
Solution: Here,
Side of square (l) = 8 cm
∴ Area of square (A1) = l2
= (8 cm)2
= 64 cm2
Radius
of quarter circle (r) = 8/2 = 4 cm
Area
of 4 quarter circles (A2) = Area of one full circle
= πr2
= 22/7 × 42
= 50.28 cm2
∴ Area of shaded region (A) =
A1 – A2
= 64 cm2 – 50.28 cm2
= 13.72 cm2
Solution: Here,
Length of rectangle (l) = 14
cm
Breadth of rectangle (b) = 7
cm
∴ Area of rectangle (A1) = l × b
= 14 cm × 7 cm
= 98 cm2
Radius
of each half circle (r) = 7/2 = 3.5 cm
Area
of 4 half circles (A2) = Area of two full circle
= 2 × πr2
= 2 × 22/7 × (3.5)2
= 77 cm2
∴ Area of shaded region (A) =
A1 – A2
= 98 cm2 – 77 cm2
= 21 cm2
You can comment your
questions or problems regarding the area
of circle here.
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