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 circle’s circumference to its diameter. It’s approximate value is 3.14159 or 22/7. It is represented by the Greek letter ‘𝛑’ and is pronounced as ‘Pie’.
- 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, 𝛑 = Circumference / Diameter
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 𝛑 is constant regardless of the size of the circle.
- The value of ‘pi’ is constant but it is called an irrational number as an exact value for ‘pi’ 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 = 𝛑d = 2𝛑r where d is the diameter and r is the radius of the circle
- Area of a circle = 𝛑r2 where r is the radius of the circle
- Volume of a sphere = 43𝛑r3 where r is the radius of the sphere
- Surface area of the sphere = 4𝛑r2 where r is the radius of the sphere
Q1: Find the circumference of a circle with diameter 40 cms.
Circumerference of a circle = 𝛑d
= 3.14 x 40 = 125.6 cms
Q2: Find the circumference of a circle with radius 10 cms.
Circumerference of a circle = 2𝛑r
= 2 x 3.14 x 10 = 62.8 cms
Q3: Find the area of a circle with radius 10 cms.
Area of a circle = 𝛑r2 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.
Circumerference the circle with diameter 10 cms = 𝛑d = 3.14 x 10 = 31.4 cms
Circumerference the circle with diameter 5 cms = 𝛑d = 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?
Area of the circle = 𝛑r2 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 = 𝛑r2: : 4r2 = 𝛑 : 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.
Area of the outer circle = 𝛑r2 where r is the radius of the circle
= 3.14 x 10 x 10 = 314 square cms
Area of the inner circle = 𝛑r2 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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