How to find the area of a circle.

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The Area of a circle.

Area is the measure of a certain surface bounded by certain limits. It is a derivative quantity of length. The SI unit of area is square meter (m^2), other measures are cm^2, km^2,Ares, ha, etc.

A circle is a round shape consisting of a curved line that completely binds a space and is the same distance from the center at every point of origin. Has a circular shape.

 The area of a circle “A” with radius “r” is given by, A=Ï€r^2.

The area of a sector subtends 360° at the center of the origin. Then,

360° corresponds to Ï€r^2.

0° corresponds to (0/360°)×Ï€r^2.

10° corresponds to (10/360°)×Ï€r^2.

180° corresponds to (180/360°)×Ï€r^2.

Hence, the area of a sector subtending to a certain angle ∅ is given by ; 

A=(∅ /360°)×Ï€r^2.


Example 1.

Find the area of a circle with radius 14 m and subtend to 90° from the origin. (use Ï€= 22/7).

Solution

Area of a circle A =(∅/360°)×Ï€r^2.

A=(90°/360)×22/7 ×(14 m)^2=

153.999999999 m^2.


Example 2.


Find the area of the circle with a radius of 70 cm and subtend to 180° from the origin.(use Ï€= 3.14).

Solution

Area of a circle A =(∅/360°)×Ï€r^2.

A=180°/360°×3.14×(70 cm)^2

=7693 cm^2.

 

Example 3.


Find the area of a circle with a radius of 70 cm and subtend to 360° from the origin. (Use Ï€=22/7).

 Solution

Area of a circle A =(∅/360°)×Ï€r^2 

A=360°/360×22/7×(70 cm)^2 

=15400 cm^2.



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