Question

A circle has a circumference of 3.14 units. What is the diameter of the circle? units Show Calculator Stuck? Watch a video or use a hint.

Answer 1

We will investigate the formulation used to determine the circumference of a cricle.

An arc is defined by the two parameters:

`\begin{gathered} \text{Arc angle ( }\theta\text{ )} \\ \text{Arc radius ( r )} \end{gathered}`

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:

`\text{Circumference ( circle ) = 2}\pi r`

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:

`\begin{gathered} d\text{ = 2r} \\ OR \\ r\text{ = }(d)/(2) \end{gathered}`

We will subsitute the above relation into the formulation provided to evaluate the circumference of a circle as follows:

`\begin{gathered} \text{Circumference ( circle ) = 2}\pi(d)/(2) \\ \\ \text{Circumference ( circle ) = }\pi d \end{gathered}`

After simplification we get the formulation in terms of diameter ( d ) of a circle.

The given circumference is as follows:

`\text{Circumference ( circle ) = 3.14}`

We will use the derived formulation and the quantity given above to evaluate for the diameter ( d ) of a circle as follows:

`\begin{gathered} 3.14\text{ = }\pi d \\ \\ d\text{ = }(3.14)/(\pi) \\ \\ d\text{ }\approx\text{ 1 unit} \end{gathered}`

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:

`1\text{ unit}`