MATHEMATICS: Geometry - Area of Sector of a circle, Radian measure, Arc length, Central angle

71

By eternaltreasures


Sector of a circle


A = 1/2 sr

s = r * t


where:

A = area of a sector

s = arc length

r = radius

t = central angle, in radians


1. A jewelry craftsman wants to cut a sector with a central angle of 30 degrees of an antique gold coin 1 in diameter and to make the golden sector a pendant for a sterling silver necklace. Find the sector area of the golden pendant.

find:

A = area of the golden pendant


given:

d = 1 in

t = 30 degrees


solution:

s = r * t

s = 0.5 in * 30 deg * pi/180 deg

s =  0.5 * 30 * 3.14/180

s = 0.26 in


A = 1/2 sr

A = 1/2 * 0.26 * 0.5

A = 0.065 sq in.


check:

30 degrees is 1/12 of 360 degrees (which is 1 revolution, 1 full circle)

Area of gold coin = pi/4 * d^2

Area of gold coin = 0.785 * d^2

Area of gold coin = 0.785 * 1^2

Area of gold coin = 0.785 sq in.

but

Area of golden pendant is 1/12 times Area of gold coin

Area of golden pendant = 1/12 * 0.785

Area of golden pendant = 0.065 sq in.


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