- Circumference of Circle
- Area of a Circle
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"= 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`
Shaalaa.com | Area Related to Circles part 1 (Perimeter Circumference)
ABC is an isosceles right-angled triangle with ∠ABC = 90°. A semi-circle is drawn with AC as the diameter. If AB = BC = 7 cm, find the area of the shaded region. [Take π = 22/7]
In the adjoining figure, the radius is 3.5 cm. Find:
(i) The area of the quarter of the circle correct to one decimal place.
(ii) The perimeter of the quarter of the circle correct to one decimal place. ( Take π = `22/7`)
In the adjoining figure, the crescent is formed by two circles which touch at the point A. O is the centre of bigger circle. If CB = 9 cm and DE = 5 cm, find the area of the shaded portion.
AC and BD are two perpendicular diameter of a circle ABCD. Given that the area of shaded portion is 308 cm2 calculate:
(i) The length of AC and
(ii) The circumference of circle