Given:
Area of a sector = 64 m²
The central angle is [tex]\theta=\dfrac{\pi}{6}[/tex].
To find:
The radius or the value of r.
Solution:
Area of a sector is:
[tex]A=\dfrac{1}{2}r^2\theta[/tex]
Where, r is the radius of the circle and [tex]\theta [/tex] is the central angle of the sector in radian.
Putting [tex]A=64,\theta=\dfrac{\pi}{6}[/tex], we get
[tex]64=\dfrac{1}{2}r^2\times \dfrac{\pi}{6}[/tex]
[tex]64=\dfrac{\pi}{12}r^2[/tex]
[tex]64\times \dfrac{12}{\pi}=r^2[/tex]
[tex]\dfrac{768}{\pi}=r^2[/tex]
Taking square root on both sides, we get
[tex]\sqrt{\dfrac{768}{\pi}}=r[/tex]
[tex]16\sqrt{\dfrac{3}{\pi}}=r[/tex]
Therefore, the value of r is [tex]16\sqrt{\dfrac{3}{\pi}}[/tex] m.
