Pi Formula

Pi formula relates the circumference and diameter of a circle. It can be used to calculate the value of pi if the measurements of circumference and diameter of a circle are given. Pi is a Greek letter, its symbol is π and in geometry, it is the ratio of the circumference of any circle to the diameter of that circle. In decimal form, the value of pi is approximately 3.14159... It cannot be written as an exact decimal as it has digits that go on forever. Let us learn about the pi formula with few solved examples at the end.

What is Pi Formula?

Pi, being an irrational number, cannot be expressed as a common fraction. Although fractions such as 22/7 are commonly used to approximate it, the exact value of pi, which is a non-terminating non-repeating decimal, can be calculated using the pi formula. No matter how large or small a circle is, the circumference divided by the diameter of a circle is always π. Pi formula can be expressed as,

Pi (π) formula = (Circumference / Diameter) 

Other Formulas With Pi

There are some basic formulas in geometry that have Pi. The formulas are:

• The perimeter of a circle is 2πr.
• The area of a circle is πr².
• Volume of a sphere is 4/3πr³.
• Surface area of a sphere is 4πr².

Where 'r' is the radius of a circle or Sphere.

Let us have a look at a few solved examples on the pi formula to understand the concept better.

Examples on Pi Formula

Example 1: Noah measured the perimeter of the circular section of pipe as 88 inches. Calculate the diameter of the same pipe using the pi formula. (Use π = 3.14 )

Solution: 

To find: The diameter of the pipe.
The perimeter of a circular pipe = 88 inches (given)
Using pi formula,
Pi(π) = (Circumference / Diameter)
3.14 = ( 88 / Diameter)
Diameter = (88 / 3.14)
= 28.02
= 28 inches (approx).

Answer:  The diameter of the pipe is 28 inches (approx).

Example 2: The diameter of a circular park measures 200 inches. Using Pi formula calculate how much distance have you covered if you walked exactly 1 round across its boundary. (Use π = 3.14 )

Solution: 

To find: Circumference of the park.
The diameter of a park = 200 inches.
Using pi formula,
Pi(π) = (Circumference / Diameter)
3.14 = (Circumference / 200)
Circumference = (3.14 × 200) inches.
= 628 inches

Answer: Total distance walked is 628 inches.

Example 3: James measured the perimeter of the circle as 66 units and the diameter of the same circle is 21 units. Using the Pi formula verify the value π = 3.14 or 22/7.

Solution: 

To find: The diameter of the circle = 21 units.
The perimeter of a circular pipe = 66 units (given)
Using pi formula,
Pi(π) = (Circumference / Diameter)
Pi(π) = 66/21 = 3.14(approx)

Hence proved.