Solve the problem.
-A circular sector has an area of $486 \mathrm { ft } ^ { 2 }$. The radius of the circle is 9 feet. What is the arc length of the sector?
A) $110 \mathrm { ft }$
B) $12 \mathrm { ft }$
C) $108 \mathrm { ft }$
D) $54 \mathrm { ft }$

Question

Quizplus · Accepted Answer

The area of a sector of a circle is given by the formula $A = \frac{1}{2} r^2 \theta$, where $A$ is the area, $r$ is the radius, and $\theta$ is the central angle in radians. Given $A = 486 \, \text{ft}^2$ and $r = 9 \, \text{ft}$, we can solve for $\theta$. First, rearrange the formula to solve for $\theta$: $\theta = \frac{2A}{r^2}$. Substituting the given values, $\theta = \frac{2 \times 486}{9^2} = \frac{972}{81} = 12 \, \text{radians}$. The arc length $L$ of a sector is given by $L = r\theta$. Substituting $r = 9 \, \text{ft}$ and $\theta = 12$, we get $L = 9 \times 12 = 108 \, \text{ft}$.

Solve the Problem 486ft2486 \mathrm { ft } ^ { 2 }486ft2

Solve the Problem $486 \mathrm { ft } ^ { 2 }$