Question

Find the Arc length and the area of the sector. Leave your answer in reduced fraction form in terms of pi.

Answer 1

Given

`\begin{gathered} r=9cm \\ _\theta=45^0 \end{gathered}`

Part A

The formula of length of an arc

`Length\text{ of an arc=}(\theta)/(360)*2\pi r`

Substitute the given into the formula

`\begin{gathered} Length\text{ of the arc=}(45)/(360)*2*\pi*9 \\ Length\text{ofthearc=}(1)/(8)\text{*2\pi*9} \\ \\ Length\text{ofthearc=}(1)/(8)*18\pi \\ \\ The\text{ length of the arc=}(9)/(2)\pi\text{ or 2}(1)/(4)\pi cm \end{gathered}`

Part b

Area of a sector

`\begin{gathered} Area\text{ of sector =}(\theta)/(360)*\pi r^2 \\ \\ \end{gathered}`

Substitute the given into the formula

`\begin{gathered} Area\text{ of sector=}(45)/(360)*\pi*9^2 \\ \\ Area\text{ofsector=}(1)/(8)*\pi*81=(81\pi)/(8)\text{ or 10}(1)/(8)\pi cm^2 \\ \end{gathered}`

Part C

`m\angle AB=45^0`