Question

find the sector area of the circle. use 3.14 for the value of π. round your answer to the nearest tenth.
11 ft
150°

a. 837.8 ft²
b. 69.1 ft²
c. 158.3 ft²
d. 380.1 ft²

Explanation:

Step1: Recall sector - area formula

The formula for the area of a sector of a circle is $A=\frac{\theta}{360^{\circ}}\times\pi r^{2}$, where $\theta$ is the central - angle of the sector in degrees and $r$ is the radius of the circle.

Step2: Identify the values of $\theta$ and $r$

Given that $\theta = 150^{\circ}$ and $r = 11$ ft, and $\pi=3.14$.

Step3: Substitute the values into the formula

$A=\frac{150^{\circ}}{360^{\circ}}\times3.14\times(11)^{2}$.
First, calculate $(11)^{2}=121$. Then, $\frac{150}{360}=\frac{5}{12}$.
So, $A=\frac{5}{12}\times3.14\times121$.
$A=\frac{5\times3.14\times121}{12}=\frac{5\times379.94}{12}=\frac{1899.7}{12}\approx158.3$ $ft^{2}$.

Answer:

C. $158.3$ $ft^{2}$