Advertisement Remove all ads

Area of Circle

Advertisement Remove all ads

Topics

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

notes

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).

Radius, r = 30 cm

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

If you would like to contribute notes or other learning material, please submit them using the button below.

Video Tutorials

We have provided more than 1 series of video tutorials for some topics to help you get a better understanding of the topic.

Series 1


Series 2


Shaalaa.com | Areas Related to Circles Ex 12 1 , Q1

Shaalaa.com


Next video


Shaalaa.com


Areas Related to Circles Ex 12 1 , Q1 [00:03:15]
S
Series:
0%


Areas Related to Circles Ex 12 1 , Q1
00:03:15 undefined
Areas Related to Circles Ex 12 1 , Q2
00:03:04 undefined
Areas Related to Circles Ex 12 1 , Q4
00:06:26 undefined
Areas Related to Circles Ex 12 1 , Q5
00:02:07 undefined
Areas Related To Circles Ex 12.2 Q1
00:01:33 undefined
Areas Related To Circles Ex 12.2 Q2
00:03:10 undefined
Areas Related To Circles Ex 12.2 Q3
00:04:49 undefined
Areas Related To Circles Ex 12.2 Q4
00:06:23 undefined
Areas Related To Circles Ex 12.2 Q5
00:06:50 undefined
Areas Related To Circles Ex 12.2 Q6
00:05:58 undefined
Areas Related To Circles Ex 12.2 Q7
00:06:05 undefined
Areas Related To Circles Ex 12.2 Q8
00:05:24 undefined
Areas Related To Circles Ex 12 2 Q9
00:04:51 undefined
Areas Related To Circles Ex 12.2 Q10
00:03:27 undefined
Areas Related To Circles Ex 12.2 Q11
00:04:10 undefined
Areas Related To Circles Ex 12.2 Q12
00:03:34 undefined
Areas Related To Circles Ex 12.2 Q13
00:06:37 undefined
Areas Related To Circles Ex 12.2 Q14
00:02:05 undefined
Areas Related To Circles Exercise 12.3 Q1
00:07:57 undefined
Areas Related To Circles Exercise 12.3 Q2
00:04:15 undefined
Areas Related To Circles Exercise 12.3 Q3
00:03:42 undefined
Areas Related To Circles Exercise 12.3 Q4
00:05:01 undefined
Areas Related To Circles Exercise 12.3 Q5
00:05:47 undefined
Areas Related To Circles Exercise 12.3 Q6
00:08:27 undefined
Areas Related To Circles Exercise 12.3 Q7
00:04:57 undefined
Areas Related To Circles Exercise 12.3 Q9
00:05:35 undefined
Areas Related To Circles Exercise 12.3 Q10
00:06:19 undefined
Areas Related To Circles Exercise 12.3 Q11
00:03:34 undefined
Areas Related To Circles Exercise 12.3 Q12
00:04:25 undefined
Areas Related To Circles Exercise 12.3 Q13
00:05:10 undefined
Areas Related To Circles Exercise 12.3 Q14
00:05:18 undefined
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×