Answer:
a) 29.45 cm (2 dp)
b) 220.89 cm² (2 dp)
Step-by-step explanation:
Formula
[tex]\textsf{Arc length}=r \theta[/tex]
[tex]\textsf{Area of a sector}=\dfrac{1}{2}r^2 \theta[/tex]
[tex]\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in radians)}[/tex]
Calculation
Given:
- [tex]\theta=\dfrac{5 \pi}{8}[/tex]
- r = 15 cm
[tex]\begin{aligned}\implies \textsf{Arc length} & =r \theta\\& = 15\left(\dfrac{5 \pi}{8}\right)\\& = \dfrac{75}{8} \pi \\& = 29.45\: \sf cm\:(2\:dp)\end{aligned}[/tex]
[tex]\begin{aligned} \implies \textsf{Area of a sector}& =\dfrac{1}{2}r^2 \theta\\\\ & = \dfrac{1}{2}(15^2) \left(\dfrac{5 \pi}{8}\right)\\\\& = \dfrac{225}{2}\left(\dfrac{5 \pi}{8}\right)\\\\ & = \dfrac{1125}{16} \pi \\\\& = 220.89 \: \sf cm^2\:(2\:dp)\end{aligned}[/tex]
