The length and area of a circular sector of radius r and angle a are given by:
[tex]\begin{gathered} S=2\pi r\cdot\frac{a}{360^{\circ}}, \\ A=\pi r^2\cdot\frac{a}{360^{\circ}}\text{.} \end{gathered}[/tex]In this problem we have:
• a = 50°,
,• r = 30 cm.
Replacing these values in the formulas above, we get:
[tex]\begin{gathered} S=2\pi\cdot(30\operatorname{cm})\cdot\frac{50^{\circ}}{360^{\circ}}\cong26.1799\operatorname{cm}\cong26\operatorname{cm}, \\ A=\pi\cdot(30\operatorname{cm})^2\cdot\frac{50^{\circ}}{360^{\circ}}\cong392.699cm^2\cong393cm^2\text{.} \end{gathered}[/tex]Answers
• S = length = 26cm,
,• A = area = 393cm².