**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 circleβs circumference to its diameter. Itβs approximate value is 3.14159 or 22/7. It is represented by the Greek letter βπβ and is pronounced as βPieβ.

- 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

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 π is constant regardless of the size of the circle.

- The value of βpiβ is constant but it is called an
*irrational*number as an exact value for βpiβ 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

**Practice Questions**

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

Answer:

Circumerference of a circle = πd

= 3.14 x 40 = 125.6 cms

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

Answer:

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.

Answer:

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.

Answer:

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?

Answer:

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.

Answer:

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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