Value of Pi

Pi is an irrational number as the number after the decimal point is never ending and cannot be used as a common fraction. 22/7 is used often for calculating Pi on an everyday basis. There is no exact value of Pi due to the infinite decimals.

How do we calculate Π ?
π= Circumference
Diameter
π= 3.14159

However, the circumference of a circle is the arc length of a circle around its perimeter. The diameter of a circle can be calculated by multiplying the radius of circle X 2.

Similarly, for calculation of the area of the circle, the value of Pi is used. The area of a circle is defined as:
Area of a circle = Pi * r * r
Where Pi = 3.14159 and r is the radius of the circle which is half the diameter of the circle.

Example: A boy walks around a circular garden with diameter 100m. Calculate the total distance covered if he completes one complete round of the garden?

Solution: When the boy completes one round of the garden, the boy covers a distance equal the circumference of the circle. Hence, we need to calculate the circumference of the garden. 

The circumference of a circle =π X diameter
                     = π X 100m
                      = 3.14159 x 100m
                      = 314.16m

So, the boy covers a distance of 314.16m when he covers one complete round of the garden.

Following are the pre-requisites that have to be kept in mind while calculating the value of PI.

1. Pi can be calculated only if the figure is an exact circle. One cannot calculate Pi for eclipses or ovals. A circle is formed when all points on the plane are on an equal distance from a single center point.

2. It is very important to have an exact measurement or value of the circumference of a circle to arrive at the value of Pi. The circumference of a circle is the length of the circle around its edges.

The circumference of the circle =πd
(D is the diameter of the circle)

3. The diameter of the circle should be measured accurately to get the exact value of Pi. The diameter can be obtained by measuring a circle from one side to its other side through the center point. You can also get the diameter of a circle by multiplying the radius of the circle by 2.

 The diameter of circle =2πR
(R is the radius of the circle)

4. It is very important to use the formulae correctly to arrive at the accurate results. You should be careful while calculating the value of circumference or diameter to avoid any errs.

5. The value arrived after dividing the circumference of the circle to its diameter will be approximately 3.14 irrespective of the size of the circle. The ratio of the two remains the same.

6. Pi is most commonly used to compute calculations concerning circles.

7. Pi is also used in several mathematical calculations such as the sum of the infinite series.

8. Due to the digitalization and modernization, we are now acquainted with around the first six billion digits of Pi.

The value of Pi has a very important place in mathematics and has proved to be of great help to arrive at the exact calculations over the period of time. The value of Pi has helped to solve various tough equations. It would have been impossible to get the accurate answer of several trigonometric and geometric equations without the value of Pi. Therefore it is very important to know the value of Pi and practice the same.

Pi comes into picture everywhere there is a circle or a circular bend. For example- the disk of the sun, the spiral of the DNA double helix, the pupil of the eye, the concentric rings that travel outward from splashes in ponds.

In physics as well, Pi plays an important role to describe waves, energy waves of light and sound. To calculate electrons and even computation of Heisenberg’s uncertainty principle, the value of Pi comes into the picture. 

Thus, everywhere in nature and the universe, Pi appears everywhere and hence the Pi has intrigued mathematicians and physicians everywhere.

1. A water sprinkler can spray water at a maximum distance of 12 m in four directions. What is the area of the garden the sprinkler can cover? Provide answer is square meters.

Solution
Since a water sprinkler covers a circular area, one rotation of the sprinkler will cover an area that will be equal to the area of the circle traversed by the sprinkler.

Area of the circle = Pi * r * r
Here, r = 12 m. So, the area of the circle will be
Π* 12 * 12 = 144 π = 452 square meters
So, the area of the garden irrigated by this water sprinkler is 452 sq. mts.

1. If the area of a circular flower garden is 5 square meters, how much fencing will be needed for the circular flower garden (round your answer to the nearest meter.)

Solution
Since the garden is circular, the fencing will be put up on the length equal to the circumference of the circle. To calculate the circumference, one needs to know the radius of the circle. 

Since, the area of the circle is known, we shall calculate radius using the area.
Area of a circle = Pi * r * r
   5= Pi *r * r = 5
                  So, r*r = 5 / Pi
r = Sqrt (5 / Pi) = 1.26 meters
Now, that we know the radius of the circle, we can now compute the circumference of the circle by the formula:
Circumference of a circle = 2 * Pi * r
                    = 2 * 3.1415 * 1.26
                    = 8 meters (rounded to the nearest digit)
The length of the fencing needed is equal to 8 meters

2. If the radius of a circular disk is increased by 20%, what is the percent increase in the area of the disk?

Solution
Assume that r is the radius of the disk, its area (before increase) is equal to
Original Area = Pi* r * r
If r is increased by 20% it becomes, the new radium becomes
r + 20% * r = r + (20/100) r = r + 0.2 r = 1.2 r
The new area after increase becomes
Pi * 1.2 r * 1.2r = 1.44* Pi* r * r
Change in area= Area after increase - Area before increase
= 1.44 *Pi* r * r - Pi* r * r
= Pi* r* r* (1.44 - 1)
 = 0.44* Pi* r * r
Percent change in area = (Change in area / original area) × 100% =
= (0.44* Pi*r * r/ Pi*r * r) × 100%
= 0.44 × 100% = 44%
Thus, the area of the disk increases by 44% if the radius is increased by 20%.