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Elementary Geometry for College St...
Solutions
Elementary Geometry for College St...
Find the approximate perimeter of the sector shown. Answer to the nearest hundredth of an inch.
To find:
The approximate perimeter of the sector.
Definition:
Arc Measure:
In a circle, the degree measure of an arc is equal to the measure of central angle that intercepts the arc.
Formula:
Perimeter of sector:
If r is the radius of circle,
Thus,
Length of an arc:
In a circle whose circumference is
We know that, circumference of a circle is given by
Hence, length
Calculation:
Perimeter of sector:
From the diagram it is clear that radius of the circle is
The measure of central angle is given as
As per the definition of measure of an arc, the degree measure of an arc is equal to the central angle intercepted by it.
Thus, the degree measure of arc =
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