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Sagot :
We will investigate the formulation used to determine the circumference of a cricle.
An arc is defined by the two parameters:
[tex]\begin{gathered} \text{Arc angle ( }\theta\text{ )} \\ \text{Arc radius ( r )} \end{gathered}[/tex]The arc angle of a complete circle is defined to be 360 degrees. To determine the circumference of a circle or perimeter of a cricle we use the following formulation:
[tex]\text{Circumference ( circle ) = 2}\pi r[/tex]We are to determine the diameter ( d ) of a circle given the circumference. The diameter ( d ) of a circle is related to the raidus ( r ) of a circle by the following relation:
[tex]\begin{gathered} d\text{ = 2r} \\ OR \\ r\text{ = }\frac{d}{2} \end{gathered}[/tex]We will subsitute the above relation into the formulation provided to evaluate the circumference of a circle as follows:
[tex]\begin{gathered} \text{Circumference ( circle ) = 2}\pi\frac{d}{2} \\ \\ \text{Circumference ( circle ) = }\pi d \end{gathered}[/tex]After simplification we get the formulation in terms of diameter ( d ) of a circle.
The given circumference is as follows:
[tex]\text{Circumference ( circle ) = 3.14}[/tex]We will use the derived formulation and the quantity given above to evaluate for the diameter ( d ) of a circle as follows:
[tex]\begin{gathered} 3.14\text{ = }\pi d \\ \\ d\text{ = }\frac{3.14}{\pi} \\ \\ d\text{ }\approx\text{ 1 unit} \end{gathered}[/tex]The value of greek symbol ( pi ) and the value of decimal point ( 3.14 ) are approximately equal. Therefore, the approximated value for the diameter ( d ) of the circle can be given as:
[tex]1\text{ unit}[/tex]
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