Class 08 Project 02

VALUE OF

BACKGROUND

In a circle, the ratio of the circumference to its diameter is a constant and is

denoted by Greek lettern. For calculation purpose, value of is generally

taken as or 3.14.

OBJECTIVE

In this project, an attempt has been made the value of using simple different met NCERT

DESCRIPTION

Method-1

Take a circular disc. Mark a point on the edge of the disc. Take a cardboard of convenient size and paste a white paper on it. Draw a line on the paper. Mark a point P on the line. Place the card on the line such that the point marked on it touches the point marked on the line. (Fig. 1). Now roll the card along the line till its marked point again touches the line at some point Q (Fig. 2).

Mathematics

PQ is the circumference of the disc. Denote it by c. Measure the diameter of

the circular disc and denote it by d. Find the ratio which is equal to t

293

Thus n=

On actual measurement:

c=21.9 cm

d= 7.0 cm

So, x=

Method-2:

A Take a squared paper of dimensions say 20 cm x 20 cm. of radius say 8 em on it as shown in Fig. 3. draw a circle

21.9

= 3.13 approx.

50/5

1:00 1

4ill 57% 4.57%

рах

LTE B

← Activities(...

Count the number of complete squares inside the circle and denote it

by a

Count the number of squares through which the circle passes and denote

it by h Find +

In this case, a = 14 x 6+12x4+ 10 x 2+6x2=164

b= 60

b So a+ 164+ 60 = 164 +30= 194

2

That is area of the circle 194 sq. units approx.

Divide a+ by (radius)", to get approximate value of r

2

Fig. 4

295

Mathematics

194 1.e. 3.03125 (approx.).

194 64

8 Again draw a circle of radius 10 cm on the squared paper and repeat

B

the above process to find value of .

In this case,

a = 18 x8 + 16 x 4 + 14 x 2 + 12 x2+8x2 = 276

b= 68

68 So a+ =276+ 310

Thus = 310 310 3.1 approx.

10 100 As radius r increases, the value of it comes closer to 3.1

Method-3:

Take a squared paper of dimension say 20 cm

cm. L

Divide a by r" to get value of it.

radius say 10 cm on it as shown in Fig. 4. Count the number of vertices of the in the circles. Let it be

Un this case. fillos increases, the value of comes closer to 3.14.

= = 3.03125 (approx.

i.e. 194 194

8- 64

).

Again draw a circle of radius 10 cm on the squared paper and repeat

the above process to find value of a.

In this case.

a = 18x8 +16x4+14x2+12x2+8x2=276

b= 68

So a+=276+ 68 = 310

Thus

310

10

310

100

3.1 approx.

As radius r increases, the value of it comes closer to 3 

Method-3:

Take a squared paper of dimension 20 cm

radius say 10 cm on it as shown in Fig. 4.

Count the number of vertices of the s

Divide a by to get value of n

In this case, m rellished 3.17

317 317 1001

10

As radius r increases, the value of comes closer to 3.14.

CONCLUSION 

The ratio of the circumference and diameter of a circle is always constant

and is denoted by . Its approximate value is 3.14.