Question

this exercise involves the formula for the area of a circular sector. a sector of a circle of radius 80 mi has an area of 1100 mi². find the central angle (in radians) of the sector. rad resources read it master it

Explanation:

Step1: Recall the area - formula for a circular sector

The formula for the area $A$ of a circular sector with radius $r$ and central - angle $\theta$ (in radians) is $A=\frac{1}{2}r^{2}\theta$.

Step2: Rearrange the formula to solve for $\theta$

Given $A = 1100$ and $r = 80$, we can rewrite the formula $\theta=\frac{2A}{r^{2}}$.

Step3: Substitute the given values into the formula

Substitute $A = 1100$ and $r = 80$ into $\theta=\frac{2A}{r^{2}}$. Then $\theta=\frac{2\times1100}{80^{2}}=\frac{2200}{6400}=\frac{11}{32}$ rad.

Answer:

$\frac{11}{32}$