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r: radius

d: diameter

A: Area

The area of a circle is given by:

*A = Π ∙ r*^{2} or A = Π ∙ (d/2)^{2}

Π defines the ratio of any circle's circumference to its diameter and is approximately equal to 3.141593, however the value 3.14 is often used.

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**Example 1:** The diameter of a circle is 16 inches. What is the lateral area?**
**

__Solution__**:**** ***A = Pi * r*^{2}**
**

*Radius = d/2 = 16/2 = 8
*

*A = 3.14 * 8*^{2}

*A = 3.14 * (64)
*

*A = 200.96 cm*^{2}*
*

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**Example 2: **From a circular sheet of radius 6 cm, a circle of radius 3 cm is removed. Find the area of the remaining sheet.

__Solution__: Here, outer radius, R = 6 cm

Inner Radius, r = 3 cm

Area of remaining sheet = Outer area - Inner area

*= Pi * (R*^{2} - r^{2})

* = 3.14 ( 6*^{2 }- 3^{2})

* = 3.14 (36 - 9)
*

* = 3.14 x 27
*

* = 84.78 cm*^{2}

Hence the area of remaining sheet is 28.26 cm^{2}

**Example 3: **Find the radius of the circle when its area is known to be 56.52 square centimeters.

__Solution__**:** We know that the area of the circle is given by: *A = Pi * r*^{2}

Isolating r we will get: *r*^{2} = A / Pi or r = √(A/Pi)

Thus:

*r = √(56.52/3.14) = √(18) centimeters**
*

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**Example 4: **Vandana uses a lawn sprinkler to water the circular region of the lawn having 30 ft in diameter. Calculate the area watered on the lawn. __
__

__Solution__**:**

Step 1: The shape of watered region is circular. Formula for area A = Pi * r^{2 }where r is the radius of the circle.

Step 2: The diameter of the circular region is 30 ft i.e. r = 30/2 = 15ft

*A = Pi * r*^{2}

*= 3.14 * 15*^{2}

*=**706.5 ft*^{2
}

**Example 5:** Determine the area of a circle whose radius is 5 meter.

*A =** **Π** **∙ r*^{2}^{ }*= 3.14 ∙ 5*^{2}^{ }*= 78.5 m*^{2}

**Example 6:** Determine the area of a circle whose diameter is 10 meter.

*A =** **Π** **∙ (d/2)*^{2}^{ }*= 3.14 ∙ (10/2)*^{2}^{ }*= 78.5 m*^{2}

Note that radius = diameter / 2

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