# Pi Formulas

Last Updated : 24 Jan, 2024

The Pi formula is used to calculate the value of Pi(Ï€). If the circumference and diameter of a circle are known, we can use them to compute the value of Pi(Ï€). Pi is a Greek letter whose sign is Ï€, and it is the ratio of the circumference of any circle to its diameter in geometry.

### Pi value in a fraction

Pi valueÂ in fraction form is 22/7. Pi is an irrational number, which shows whether the digit after the decimal is infinite or the final value, As a result, 22/7 is used in everyday computations. “Ï€”Â is an irrational number since it is not equal to the ratio of any two numbers. The numeric value of Pi is 3.14159… It cannot be represented as an exact decimal since the digits continue indefinitely. Pi (Ï€) is the ratio of a circle’s circumference to its diameter and is approximately equal to 3.14159. In a circle, dividing the circumference (the entire distance around the circle) by the diameter yields the same result. The value of pi remains constant regardless of the size of the circle. Pi is represented by the symbol Ï€.

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The formula of Pi can be expressed as,

Circumference / Diameter = Ï€

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â = 3.14159… or 22/7

### We have some other Pi formulas

Circumference of Circle = 2Ï€r

Â  Â  Â  Â  Â  Â  Â  Â  Â Area of circle = Ï€r2Â

Â  Â Surface Area of Circle = 4Ï€r2

Â  Â  Â  Â  Â  Â  Volume of a sphere = 4/3 Ï€r3

### Some Examples Related to Pi Formula

Example 1: A person measured the perimeter of the circular section of pipe as 84 inches. Calculate the diameter using the pi formula?

Solution:

Given: The perimeter of a circular pipe = 84 inches

By Using pi formula,

We have ,

Â  Â  Â  Â  Pi(Ï€) = (Circumference / Diameter)

Â  Â  Â  Â  Â 3.14 = (84 / Diameter)

Diameter = (84 / 3.14)

Â  Â  Â  Â  Â  Â  Â  Â = 26.75

Â  Â  Â  Â  Â  Â  Â  Â = 27 inches (approx).

Therefore the diameter Â of pipe is 27 inches .

Example 2: If the Radius of the circular shape is 5 cm then find out the circumference by using the pi formula?

Solution:

Given: The radius of a circular shape (r) = 5 cm

then diameter = 2r

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â = 2 Ã— 5

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â = 10 cm

By Using pi formula,

We have ,

Â  Â  Â  Â  Â  Â  Â Â  Â Pi(Ï€) = (Circumference / Diameter)

Â  Â  Â  Â  Â  Â  3.1415 = (circumference / 10)

circumference = (3.14 Ã— 10)

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â = 31.4 cm

Therefore the circumference of circular shape is 31.4 cm .

Example 3: If the Radius is 6 cm then find out the circumference by using the pi formula?

Solution:

Given: The radius of a circular shape (r) = 6 cm

then diameter = 2r

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  = 2 Ã— 6

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  = 12 cm

By Using pi formula,

We have ,

Â  Â  Â  Â  Â  Â  Â  Â  Pi(Ï€) = (Circumference / Diameter)

Â  Â  Â  Â  Â  Â  3.1415 = (circumference / 12)

circumference = (3.14Ã— 12)

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  = 37.68 cm

Therefore the circumference of circular shape is 37.68 cm .

Example 4: A perimeter of the ball is 70 cm. Calculate the diameter of the same using the pi formula. ?

Solution:

Given: The perimeter of a ball = 70 cm

By Using pi formula,

We have ,

Â Â  Â  Pi(Ï€) Â = (Circumference / Diameter)

Â  Â 3.1415 = (70 / Diameter)

Diameter = (70 / 3.14)

Â  Â  Â  Â  Â  Â  Â  Â = 22.29 cm

Therefore the diameter of ball is 22.29 cm Â .

Example 5: If the diameter is 7 cm find out its circumference?

Solution:

Â Given: diameter = 7 cm

To find the circumference?

Â  Â  Â  Â  Â  Â  Â  Â  Â Â Pi(Ï€) = (Circumference / Diameter)

Â  Â  Â  Â  Â  Â  Â  3.1415 Â = (Circumference / 7)

Â  Â  circumference = (3.14 Ã— 7)

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  = 21.98 cm

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  = Â 22 cm

Example 6: A circle has a radius of 5 cm. Calculate its diameter, area, and circumference?

Solution:

Â Given: Radius(r) = 5 cm

Â  Â  Â  Â  Diameter of a circle = 2r

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  = 2 Ã— 5 cm

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  = 10 cm

Â  Â To find: Area of a circle Â = Â Ï€ 52

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â = Ï€ Ã— 25

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â = 3.14159 Ã— 25 cm2

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â = 78.54 cm2

Â  Circumference of a circle = 2 Ï€ r

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â = 2 Ã— Ï€ Ã— 5

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â = 10 Ã— 3.14159 Â cm

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â = 31.4159 cm

Example 7: Â Find the volume of a sphere whose radius is 6 cm?

Solution:

Â Given: Radius, r = 6 cm

Volume of a sphere = 4/3 Ï€r3 units3

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  V = 4/3 Ã— 3.14 Ã— 63

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â V = 4/3 Ã— 3.14 Ã— 216

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â V = Â 2712.96 / 3

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â V = 904 .32 cm3