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Perimeter and Area of a Circle

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  • Circumference of Circle
  • Area of a Circle

notes

1) Perimeter of a Circle- The boundary of any geometrical figure is known as perimeter of that figure. The perimeter of a circle is also known as circumference. The circumference and diameter of a circle have constant ratio.


`"circumference"/"diameter"= π`


`"circumference"= π xx diameter`
                         `= π xx 2r` (where r is the radius of the circle)
`"circumference of a circle" = 2πr`

2) Area of Circle- In geometry, the areal enclosed by a circle of radius r is `pi r^2`. Here the Greek letter `pi` represents a constant, approximately equal to 3.14159, which is equal to the ratio of the circumference of any circle to its diameter. 
You may also recall that area of a circle is `πr^2`, where r is the radius of the circle. Recall that you have verified it in Class VII, by cutting a circle into a number of sectors and rearranging them as shown in Fig.

You can see that the shape in Fig.(ii) is nearly a rectangle of length `1/2 xx 2πr` and breadth `r`.  This suggests that the area of the circle = `1/2 xx 2πr xx r= πr^2. `
Example- The cost of fencing a circular field at the rate of `₹  24` per metre is `₹  5280.` The field is to be ploughed at the rate of `₹ 0.50` per m2. Find the cost of ploughing the field `(Take   π = 22/7).`
Solution : `"Length of the fence (in metres)" = "Total cost"/"Rate"= 5280/ 24= 220`


So, circumference of the field = 220 m
Therefore, if r metres is the radius of the field, then
2πr = 220


or, `2 xx  22/7 xx r= 220`


or, ` r= "220×7"/ "2×22"= 35`


i.e., radius of the field is 35 m. 
Therefore, area of the field = `πr^2 = 22/7 xx 35 xx 35 m^2 = 22 xx 5 xx 35 m^2`
Now, cost of ploughing 1m2 of the field = `₹ 0.50`
So, total cost of ploughing the field = `₹ 22 × 5 × 35 × 0.50 = ₹ 1925`

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 | Area Related to Circles part 1 (Perimeter Circumference)

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Area Related to Circles part 1 (Perimeter Circumference) [00:06:59]
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