SOLUTION: Find the area of a sector defined by a central angle of 36 degrees and a radius of 10 cm.

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Question 87682: Find the area of a sector defined by a central angle of 36 degrees and a radius of 10 cm.
Answer by jim_thompson5910(35256) About Me  (Show Source):
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Solved by pluggable solver: Calculate area of a sector

Angle at center described by an Arc
The angle described by an arc at center is 36 degrees.



Arc of a circle
The Area of Sector is given by formula
Area=+pi%2Aradius%2Aradius%2Acentral+angle%2F360
Area+=+pi%2A10%2A10%2A36%2F360=31.4159265


Conversion of angles from degrees to radian:
The relation between two units of angle measurement is :

2*pi rad = 360 degrees


Area of Sector when angle in radians is,
Area=central+angle%2Aradius%2Aradius%2F2
Area=0.62831853%2A10%2A10%2F2=31.4159265


Hence, For a circle of radius 10 Area of sector is 31.4159265 when it subtends an angle of 36 degrees at center.

For more on this topic, See the lessons on Circles and their properties

Some relevant wikipedia articles for the topic.