The value of Pi is approximately equal to 3.14159. It is defined as the ratio of the circumference of a circle to its diameter. If we divide the total circumference of a circle by the diameter of the circle, then it will always be in a ratio of 22/7. Pi is denoted by the Greek symbol π.
Its exact value is unknown and can not be calculated by the available means as it is an irrational number, i.e. non-recurring and non-terminating decimal. We define the π as the ratio of the circumference to the diameter of a circle. It is a constant used widely in every branch of Science and Mathematics.
What is Pi?
Pi is a symbol used in Mathematics. It is represented by the symbol π. It is a ratio of the Circumference of the Circle and the Diameter of the Circle. The value of Pi is an irrational number. Thus the exact value of the π is not found yet.
We can also define π as the total number of times the diameter is wrapped around the circumference of any circle. The approximate value of (π) pi is 3.14 or 22/7. The following illustration represents the value of pi and its relation with the circumference and diameter of the circle.
Pi Values in Fraction and Decimal
We usually express the value of Pi in two ways that are
- Value of Pi in Fraction
- Value of Pi in Decimal
Approximate Value of Pi
The value of pi is non-terminating decimal and non-recurring decimal. However, the approximate value of pi (π) is commonly rounded to 3.14. Below is the approx. value of pie in fraction and decimal form.
Value of Pi (π) in Fractions
The pi value can be approximated as the fraction of 22/7. It is known that pi is an irrational number which means that the digits after the decimal point are never-ending and are a non-terminating value. Therefore, 22/7 is used for everyday calculations. ‘π’ is not equal to the ratio of any two numbers, which makes it an irrational number.
The approximate value of Pi is the value of the Pi in fractions or up to 2 decimals places. As Pi is an irrational number its exact value is not known and so we take the approximate value of Pi in our calculation. The approximate value of Pi in terms of fractions is,
π = 22/7 (Approx)
Value of Pi (π) in Decimal
The approximate value of Pi in terms of decimals is
π = 3.14 (Approx)
The pi value up to the first 100 decimal places is:
3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 . . .
The formula used to calculate the value of the Pi is
π = C/D
Where,
Using this formula we can easily get the value of pi, But as we know pi is an irrational number so its exact value is unknown and we can only find the approximate value of pi using this formula. The value of the Pi found using this formula is 3.14
How to Calculate Value of Pi?
Pi is an irrational number and it has an infinite number of decimal values that are non-repeating,. There are various methods to calculate the value of pi up to a hundredth of a place The most common method to find the value of pi is taking the ratio of the Circumference of the circle to the diameter of the circle.
π = Circumference of Circle/Diameter of Circle
Thus, by drawing various circles and then taking the ratio of the Circumference and the diameter of the circle we get the value of the circle. The table added below shows the circumference of the circle, the diameter of the circle and their ratio as well.
Circumference(C) | Diameter(D) | C/D |
|---|
3.1 | 1 | 3.1 |
6.24 | 2 | 3.12 |
9.378 | 3 | 3.126 |
12.5678 | 4 | 3.141 |
15.7075 | 5 | 3.1415 |
As we take higher values of circumference and diameter then we find to get the more accurate value of pi.
Different Values of Pi
Other then fractions and decimals there are some other values of Pi as well.
Value of Pi in Degree
The value of Pi in degrees can easily be found using the relation, of the ratio of circumference of the circle and the diameter of the circle. We know that the circumference of the circle is 2πr, and the diameter of the circle is 2r where r is the radius of the circle. Also, incase of the complete circle the angle subtended at the centre of the circle is 360°also we have two half circle in a circle that is divided by a diameter.
Now, then the ratio of the circumference and the diameter gives the value of pi.
2πr/2r = 360°/2
π radians = 180°
Also Check,
Solved Examples on Pi Value
Example 1: Find the circumference of a circle which has a radius of 12 cm.
Solution:
Given,
- Radius of Circle(r) = 12 cm
Circumference of Circle(C) = 2πr
Value of Pi = 3.14
⇒ C = 2 ⨉ (3.14) ⨉ (12)
⇒ C = 75.36 cm
Example 2: Find the area of a circle which has a radius of 8 cm.
Solution:
Given,
- Radius of Circle(r) = 8 cm
Area of Circle(A) = πr2
As, Value of Pi = 3.14
⇒ A = (3.14) ⨉ (8)2
⇒ A = 200.96 cm2
Example 3: Find the circumference and the area of the circle which has a radius of 9 cm.
Solution:
Given,
- Radius of Circle(r) = 9 cm
Circumference of Circle(C) = 2πr
Area of Circle(A) = πr2
As, Value of Pi = 3.14
⇒ C = 2 ⨉ (3.14) ⨉ (12)
⇒ C = 56.52 cm
⇒ A = π ⨉ (9)2
⇒ A = 254.34 cm2
Conclusion
Pi is an important mathematical term which has a constant and non-terminating, irrational value. It has an unending value of 3.14159 and in mathematical solutions, it is rounded off to 3.14 in terms of decimal values, or 22/7 for numerical calculations to make them easier. It is used in multiple scenarios, to calculate the areas and volumes of spheres, hemispheres, cylinders, circles etc. All those geometrical shapes that have a circle involved in their shaping use the concept and formulae regarding pi. Thus, it is important to learn the values and usages of PI since it is one of the governing factors of geometrical mathematics.
Practice Problems on Value of Pi
Problem 1: Calculate the circumference of a circle with a radius of 5 units. [Circumference = 2πr.]
Problem 2: If the diameter of a circle is 12 inches, what is its circumference? [Use the formula C = πd.]
Problem 3: Given the area of a circle is 64 square meters, find the radius. [The formula for the area of a circle is A = πr².]
Problem 4: The side of a square is equal to the diameter of a circle. If the circle's area is 144π square units, what is the side length of the square?
Problem 5: The Leibniz formula for π alternates signs in an infinite series: π/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - . . . Calculate an approximation of π using the first 10 terms of this series.
Problem 6: If the height of a cylinder is 20 centimeters and the value of it's radius across ends is 14 centimeters, calculate it's volume. [The formula for the volume of a cylinder is V = πr²h]
Problem 7: If the radius of a sphere is 30 centimeters, then calculate the volume of the sphere. [The formula for the volume of a sphere is V = 4/3πr3]
Problem 8: If the radius of a sphere is 10 meters, the calculate it's total surface area. [The formula for the total surface area of a sphere is TSA = 4*πr²]
Problem 9: Convert 270 degrees into radians. [The formula to convert degrees into radians is degrees×(π/180) = radians]
Problem 10: Convert 3π/4 radians into degrees. [The formula to convert radians into degrees is radians × (180/π)= degrees]
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