Question

What is the arc length of one slice of pie?

Answer 1

Ok, so what is this question asking?

Its asking for one piece of the circumference.

The circumference is equal to
`\pi (Diamateter)` OR
`\pi (2*radius)`

We are given the diameter.

The circumference is 10
`\pi`

The circumference is divided into six arcs.

The length of one arc is equal to the circumference divided by the number of arcs. (equal, in this case)

`(10\pi )/(6)` = 5.24

Hope this helps

:D

Answer 2

We will have the following:

First, we know that the piece are a sixth of a circle, so the angle for each slice will be:

`2\pi\ast(1)/(6)=(1)/(3)\pi`

Now, we will calculate the arc length as follows:

`\begin{gathered} s=(5in)((1)/(3)\pi)\Rightarrow s=(5)/(3)\pi in \\ \\ \Rightarrow s\approx5.24in \end{gathered}`

So, the arc length is approximately 5.24 inches.