Question

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

Answer 1

a) 29.45 cm (2 dp)

b) 220.89 cm² (2 dp)

Explanation:

Formula

`\textsf{Arc length}=r \theta`

`\textsf{Area of a sector}=(1)/(2)r^2 \theta`

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

Calculation

Given:

• 
  `\theta=(5 \pi)/(8)`
• r = 15 cm

`\begin{aligned}\implies \textsf{Arc length} & =r \theta\\& = 15\left((5 \pi)/(8)\right)\\& = (75)/(8) \pi \\& = 29.45\: \sf cm\:(2\:dp)\end{aligned}`

`\begin{aligned} \implies \textsf{Area of a sector}& =(1)/(2)r^2 \theta\\\\ & = (1)/(2)(15^2) \left((5 \pi)/(8)\right)\\\\& = (225)/(2)\left((5 \pi)/(8)\right)\\\\ & = (1125)/(16) \pi \\\\& = 220.89 \: \sf cm^2\:(2\:dp)\end{aligned}`