Question

Find (a) arc length and (b) Area of a sector.

Answer 1

a) 38.40 yd (2 dp)

b) 211.18 yd² (2 dp)

Explanation:

Formula

`\textsf{Arc length}=2 \pi r\left((\theta)/(360^(\circ))\right)`

`\textsf{Area of a sector}=\left((\theta)/(360^(\circ))\right) \pi r^2`

`\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in degrees)}`

Calculation

Given:

• 
  `\theta` = 200°
• r = 11 yd

`\begin{aligned}\implies \textsf{Arc length} &=2 \pi (11)\left((200^(\circ))/(360^(\circ))\right)\\ & = 22 \pi \left((5)/(9)\right)\\ & = (110)/(9) \pi \\ & = 38.40\: \sf yd \:(2\:dp)\end{aligned}`

`\begin{aligned} \implies \textsf{Area of a sector}& =\left((200^(\circ))/(360^(\circ))\right) \pi (11)^2\\& = \left((5)/(9)\right)\pi \cdot 121\\& = (605)/(9) \pi\\& = 211.18\: \sf yd^2 \:(2\:dp)\end{aligned}`

Please note: As you have not specified if π should be approximated, I have not used an approximation for π.