#### 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`