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# Perimeter and Area of a Circle

Course

#### description

• 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) [00:06:59]
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