Question

Find the circumference for the following circles. Either leave in terms of by entering answers with the word pi, or use 3.14 for pi and round your answer to the nearest 10th.

Answer 1

Circumference of a circle is given by

`\begin{gathered} C=2\pi r \\ \text{Where C is the circumference of the circle } \end{gathered}`

The length of an arc is given by

`\begin{gathered} l=(\theta)/(360^o)*2\pi r \\ \text{That is } \\ l=(\theta)/(360^o)* C \end{gathered}`

From the diagram given, the arc has

`\begin{gathered} A\text{ length of } \\ l=12\pi\text{ and }\theta=225^o \end{gathered}`

From here we have that

`\begin{gathered} l=(\theta)/(360^o)* C \\ 12\pi=(225)/(360^o)* C \\ 12\pi=(225C)/(360) \\ 225C=360*12\pi \\ C=(360*12\pi)/(225) \\ C=(96)/(5)\pi \end{gathered}`

Hence the answer is

`(96)/(5)\text{ pi}`