Question

radius is equal to 6 cm and area of sector is equal to 15 pie square CM then find theta and length of Arc​

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}15πcm

2

Radius ,r = 6 cm

We know that ,

Area of sector :

\begin{lgathered}\frac{\pi r^{2}\theta}{360\degree} = 15\pi \\ \\ =\ \textgreater \ \frac{6^{2} *\theta}{360} = 15 \\ \\ =\ \textgreater \ \theta = 150\degree\end{lgathered}

360°

πr

2

θ

=15π

= >

360

6

2

∗θ

=15

= > θ=150°

2) Length of arc,

\begin{lgathered}l= \frac{\pi*r*\theta}{180\degree} \\ \\ l = \frac{\pi*6* 150\degree }{180\degree} \\ \\ =\ \textgreater \ l = 5\pi cm\end{lgathered}

l=

180°

π∗r∗θ

l=

180°

π∗6∗150°

= > l=5πcm