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Pi the number

The number Pi is also called the Archimedes constant. It is a mathematical constant and is defined as the ratio of a circleโ€™s circumference to its diameter. Itโ€™s approximate value is 3.14159 or 22/7. It is represented by the Greek letter โ€˜๐›‘โ€™ and is pronounced as โ€˜Pieโ€™.

 

  • For any circle, if you divide the circumference of the circle by its diameter you will get the value Pi as the result.

 

Therefore we have, ๐›‘ = Circumference / Diameter

Where:

The circumference of a circle is the length of the edge around the circle;

The diameter of the circle is twice the radius of the circle;

The ratio ๐›‘ is constant regardless of the size of the circle.

 

  • The value of โ€˜piโ€™ is constant but it is called an irrational number as an exact value for โ€˜piโ€™ does not exist.

 

What is Pi math?

Pi is one of the most important mathematical constants and is widely used in Geometry. Common applications of the number Pi in geometry include the following formulae:

  • Circumference of a circle = ๐›‘d = 2๐›‘r  where d is the diameter and r is the radius of the circle
  • Area of a circle = ๐›‘r2 where r is the radius of the circle
  • Volume of a sphere = 43๐›‘r3 where r is the radius of the sphere
  • Surface area of the sphere = 4๐›‘r2 where r is the radius of the sphere

 

Practice Questions

Q1: Find the circumference of a circle with diameter 40 cms.

Answer:    

Circumerference of a circle = ๐›‘d

= 3.14 x 40 = 125.6 cms

 

Q2: Find the circumference of a circle with radius 10 cms.

Answer:    

Circumerference of a circle = 2๐›‘r

= 2 x 3.14 x 10 = 62.8 cms

 

Q3: Find the area of a circle with radius 10 cms.

Answer:    

Area of a circle = ๐›‘r2 where r is the radius of the circle

        = 3.14 x 10 x 10

        = 314 square cms

 

Q4: A circle has a diameter of 10 cms and a second circle has a diameter of 5 cms. Find the ratio of the circumference of the first circle to the circumference of the second circle.

Answer:

Circumerference the circle with diameter 10 cms = ๐›‘d = 3.14 x 10 = 31.4 cms

Circumerference the circle with diameter 5 cms = ๐›‘d = 3.14 x 5 = 15.7 cms

Therefore ratio of the circumference of the two circles = 31.4 : 15.7 = 2 : 1

 

Q5: Consider a circle and a square as shown below:

What is the ratio of the area of the circle to the area of the square?

Answer:

Area of the circle = ๐›‘r2 where r is the radius of the circle

Area of a square = side x side = 2r x 2r = 4r2

Therefore, ratio of the area of circle to area of square = ๐›‘r2: : 4r2 = ๐›‘ : 4    

 

Q6: Consider two concentric circles - The outer circle has a diameter of 10 cms. It has another circle inside it with radius of 5 cms. Find the area between the two circles.

Answer:

Area of the outer circle = ๐›‘r2 where r is the radius of the circle

        = 3.14 x 10 x 10 = 314 square cms

Area of the inner circle = ๐›‘r2 where r is the radius of the circle

        = 3.14 x 5 x 5 = 78.5 square cms

Therefore, the area between the two circles = area of outer circle - area of inner circle

        = 314 - 78.5 = 235.5 square cms.

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