Pi Formulas

Pi (π) is one of the most well-known mathematical constants. It represents the ratio of the circumference of a circle to its diameter. No matter the size of the circle, this ratio remains constant.

Basic Definition is given as π=C​/d where C is the circumference of the circle and d is its diameter. The concept of π has been known since ancient times, with early estimates appearing in Egyptian and Babylonian mathematics. Today, π has been calculated to trillions of digits using computers, demonstrating its irrational and non-repeating nature. Learn more about pi and its related formula in this article by Extramarks.

What is Pi?

The number pi (π) is a fundamental mathematical constant that signifies the relationship between a circle’s circumference and its diameter. It holds significant importance across different fields of mathematics and science, particularly in geometry and trigonometry.

Properties of Pi

1. Pi cannot be precisely represented as a fraction of two whole numbers. Its decimal representation goes on infinitely without any repeating pattern. Some initial digits of pi include 3.141592653589793…
2. Pi is not the root of any non-zero polynomial equation with rational coefficients. This property implies that it cannot be constructed with a finite number of steps using only a compass and straightedge.

What is Pi Formula?

The fundamental definition of π is the ratio of the circumference of a circle to its diameter. The formula of pi is given as

π=C/d​

where:

• $C$ is the circumference of the circle.
• $d$ is the diameter of the circle.

Other Formulas of Pi

Common Geometric Formulas Involving Pi

• Circumference of a Circle: C=2πr; where, r is the radius of the circle.
• Area of a Circle: A=πr²; where $r$ is the radius of the circle.
• Volume of a Cylinder: V=πr²h; where r is the radius of the base and h is the height of the cylinder.
• Surface Area of a Sphere: A=4πr²; where r is the radius of the sphere.
• Volume of a Sphere: V=4/3πr³; where r is the radius of the sphere.

Examples on Pi Formula

Example 1: Find the area of a circle with a diameter of 10 meters.

Solution:

Given d = 10 m, r = 10/2 = 5 m

Area of circle = πr² = π5² = 25π = π x 3.14 = 78.5 cm²

Example 2: Calculate the volume of a cylinder with a radius of 3 cm and a height of 10 cm.

Solution:

Given r = 3cm, h = 10 cm

Volume of cylinder = πr²h = 3.14 x 9 x 10 = 282.6 cm³

Example 3: Calculate the volume of a sphere with a radius of 4 meters.

Solution:

Given r = 4 m

Volume of Sphere = 4/3πr³

Volume = 4/3 x 3.14 x 64 = 150.72 cm³