Pi Formulas

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

Pi is represented by the symbol π. Pi (π) is the ratio of the Circumference of a Circle and Diameter of a Circle. Pi is an irrational number. Thus the exact value of the π is not found yet.

Value of Pi is generally expressed in two ways that are

• Value of Pi in Fraction
• Value of Pi in Decimal

Pi value in fraction form is 22/7

Decimal value of Pi is 3.14159… It cannot be represented as an exact decimal since the digits continue indefinitely.

Pi (π) 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.

Main formula to find value of Pi is taking the ratio of the circumference of the circle and the diameter of the circle.

π = Circumference / Diameter = 3.14159… = 22/7

The table added below shows the circumference of the circle, the diameter of the circle and their ratio as well.

Other Pi Formulas

Various other formulas which gives the value of Pi are:

• Circumference of Circle = 2πr

• Area of Circle = πr²

• Surface Area of Sphere = 4πr²

• Volume of a Sphere = 4/3 πr³

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:

• Perimeter of a circular pipe = 84 inches

By Using pi formula,

We have,

Pi(π) = (Circumference / Diameter)

3.14 = (84 / Diameter)

Diameter = (84 / 3.14)

= 26.75 = 27 inches (approx)

Therefore the diameter  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:

• Radius of a circular shape (r) = 5 cm

Diameter = 2r = 2 × 5 = 10 cm

By Using pi formula,

We have,

Pi(π) = (Circumference / Diameter)

3.1415 = (circumference / 10)

Circumference = (3.14 × 10) = 31.4 cm

Therefore, 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:

• Radius of a circular shape (r) = 6 cm
• Diameter = 2r = 2 × 6 = 12 cm

By Using pi formula,

We have,

Pi(π) = (Circumference / Diameter)

3.1415 = (circumference / 12)

Circumference = (3.14 × 12) = 37.68 cm

Therefore circumference of circular shape is 37.68 cm

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

Solution:

Given:

• Perimeter of a ball = 70 cm

By Using pi formula,

We have,

Pi(π)  = (Circumference / Diameter)

3.1415 = (70 / Diameter)

Diameter = (70 / 3.14) = 22.29 cm

Therefore the diameter of ball is 22.29 cm

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

Solution:

Given:

• Diameter = 7 cm

To find the circumference?

Pi(π) = (Circumference / Diameter)

3.1415  = (Circumference / 7)

Circumference = (3.14 × 7) = 21.98 cm =  22 cm

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

Solution:

Given:

• Radius(r) = 5 cm
• Diameter of a circle = 2r = 2 × 5 cm = 10 cm

Area of a circle  =  π r²

π 5² = π × 25

= 3.14159 × 25

= 78.54 cm²

Circumference of a circle = 2 π r

= 2 × π × 5

= 10 × 3.14159

= 31.4159 cm

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

Solution:

 Given:

• Radius, r = 6 cm

Volume of a Sphere = 4/3 πr³ units³

V = 4/3 × 3.14 × 6³

V = 4/3 × 3.14 × 216

V =  2712.96 / 3

V = 904 .32 cm³

Q1. What is the volume of a cylinder with a radius of 44 cm and a height of 10 cm? Use π = 3.14

Q2. Find the length of an arc of a circle with radius 99 cm and central angle 45^∘. Use π = 3.14

Q3. Calculate the surface area of a sphere with a radius of 66 inches. Use π = 3.14

Q4. Determine the volume of a hemisphere with a radius of 10 cm. Use π = 3.14

Q5. What is the area of a sector of a circle with a radius of 15 cm and a central angle of 120^∘? Use π = 3.14

Q6. Find the total surface area of a cone with a radius of 8 cm and a slant height of 12 cm. Use π = 3.14

What is π?

π is a mathematical constant representing the ratio of a circle’s circumference to its diameter. It is an irrational number, meaning it cannot be expressed as a simple fraction, and its decimal representation goes on infinitely without repeating.

What is the value of π?

The value of π is approximately 3.14159, but it extends infinitely. It is often rounded to π ≈ 3.14 for practical calculations.

Who discovered π?

The concept of π has been known for thousands of years. Ancient civilizations like the Indus ValleyCivilization, Egyptians and Babylonians had rough approximations of π. Greek mathematician Archimedes is credited with one of the earliest rigorous approximations of π using geometric methods.

How many digits of π are known?

With modern computational methods, trillions of digits of π have been calculated. However, for most practical purposes, a few decimal places are sufficient. As of now, the world record for the most digits of ππ calculated is in the trillions.