Answer
$60^{\circ}$
Work Step by Step
Step 1: The formula to be used here is $A=\frac{1}{2}r^{2}\theta$ where $A$ is the area of the sector of the circle of radius $r$ and central angle $\theta$.
Step 2: Substituting the values in the question, $6\pi=\frac{1}{2}(6^{2})\theta$
Step 3: Multiplying both sides by 2,
$6\pi\times2=\frac{1}{2}\times(6^{2})\times\theta\times2$
Step 4: $12\pi=36\theta$
Step 5: Multiplying both sides by $\frac{1}{36}$,
$12\pi\times\frac{1}{36}=36\theta\times\frac{1}{36}$
Step 6: $\theta=\frac{\pi}{3}$
Step 7: Converting radians to degrees,
$\frac{\pi}{3}=\frac{\pi}{3}(\frac{180^{\circ}}{\pi})=60^{\circ}$
Step 8: Therefore, the required angle is $60^{\circ}$.
