Question

The radius of a sector is 6cm and its area is πsq.cm. What is its central angle?

Answer 1

Answer:

Final Answer :   Angle of sector: 150\degree150°

                            Length of arc of sector: 5πcm 

Steps: 

1) Area of sector : 15\pi cm^{2}15πcm2  

Radius ,r = 6 cm 

We know that , 

Area of sector : 

\begin{gathered} \frac{\pi r^{2}\theta}{360\degree} = 15\pi \\ \\ =\ \textgreater \ \frac{6^{2} *\theta}{360} = 15 \\ \\ =\ \textgreater \ \theta = 150\degree \end{gathered}360°πr2θ=15π= \textgreater 36062∗θ=15= \textgreater θ=150°

2)  Length of arc,

\begin{gathered}l= \frac{\pi*r*\theta}{180\degree} \\ \\ l = \frac{\pi*6* 150\degree }{180\degree} \\ \\ =\ \textgreater \ l = 5\pi cm \end{gathered}l=180°π∗r∗θl=180°π∗6∗150°= \textgreater l=5πcm