Answer
$3.6$ radians
Work Step by Step
Step 1: The formula to be used here will be $A=\frac{1}{2}r^{2}\theta$ where $A$ is the area of a sector of a circle of radius $r$ and central angle $\theta$.
Step 2: Substituting the values provided by the question into the formula, $(16)=\frac{1}{2}(3)^{2}\theta$
Step 3: $16=\frac{9\theta}{2}$
Step 4: Multiplying both sides by $\frac{2}{9}$,
$16\times\frac{2}{9}=\frac{9\theta}{2}\times\frac{2}{9}$
Step 5: $\theta=\frac{32}{9}=3.6$ radians
