# Area of Circle

#### definition

Area of a circle: The area of a circle is the region occupied by the circle in a two-dimensional plane.

#### formula

Area of the circle = πr2

# Area of a circle:

• The area of a circle is the region occupied by the circle in a two-dimensional plane.

• Draw a circle and cut them into a number of sectors and rearranging them as shown in Figure.

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 into 64 sectors, and arrange these sectors. It gives nearly a 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 the circumference) × radius

= (1/2 × 2πr) × r

= πr2

So, the area of the circle = πr2

#### Example

Find the area of a circle of radius 30 cm (use π = 3.14).

Area of the circle = πr2

= 3.14 × 302

= 2,826 cm2

#### Example

Diameter of a circular garden is 9.8 m. Find its area.

Diameter, d = 9.8 m.
Therefore, radius r = 9.8 ÷ 2 = 4.9 m

Area of the circle = πr2

= 22/7 × (49.2)2 m2

= 22/7 × 4.9 × 4.9 m2

= 75.46 m2

#### Example

The following figure shows two circles with the same center. The radius of the larger circle is 10 cm and the radius of the smaller circle is 4 cm.

Find:
(a) the area of the larger circle
(b) the area of the smaller circle
(c) the shaded area between the two circles. (π = 3.14)

(a) Radius of the larger circle = 10 cm

So, area of the larger circle= πr2 = 3.14 × 10 × 10 = 314 cm2

(b) Radius of the smaller circle = 4 cm

Area of the smaller circle = πr2 = 3.14 × 4 × 4 = 50.24 cm2

(c) Area of the shaded region = (314 – 50.24) cm2 = 263.76 cm2

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