Answer :
Answer:
[tex]\theta=\dfrac{3\pi}{8} $ (in radians)[/tex]
Step-by-step explanation:
Area of a sector[tex]=\dfrac{\theta}{2\pi}X\pi r^2[/tex]
Given: Area of a sector [tex]=48\pi cm^2[/tex]
Radius of the circle =16cm
Therefore:
[tex]48\pi cm^2=\dfrac{\theta}{2}X 16^2\\256\theta=96\pi\\\theta=\dfrac{96\pi}{256} \\\theta=\dfrac{3\pi}{8} $ (in radians)\\Therefore, the central angle \theta=\dfrac{3\pi}{8} $ (in radians)[/tex]
