Question

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

Answer 1

a) 19.63 mm (2 dp)

b) 245.44 mm² (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` = 45°
• r = 25 mm

`\begin{aligned}\implies \textsf{Arc length} &=2 \pi (25)\left((45^(\circ))/(360^(\circ))\right)\\ & = 50 \pi \left((1)/(8)\right)\\ & = (25)/(4) \pi \\ & = 19.63\: \sf mm \:(2\:dp)\end{aligned}`

`\begin{aligned} \implies \textsf{Area of a sector}& =\left((45^(\circ))/(360^(\circ))\right) \pi (25)^2\\& = \left((1)/(8)\right)\pi \cdot 625\\& = (625)/(8) \pi\\& = 245.44\: \sf mm^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.