Question

question 4 of 10 what is the approximate area of the shaded sector in the circle shown below? 155° 4.3 in c a. 11.63 in² b. 50 in² c. 5.82 in² d. 25 in²

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 and $r$ is the radius of the circle.

Step2: Identify values

From the problem, $\theta = 155^{\circ}$ and $r = 4.3$ in.

Step3: Substitute values into formula

$A=\frac{155^{\circ}}{360^{\circ}}\times\pi\times(4.3)^{2}$.
First, calculate $(4.3)^{2}=18.49$. Then, $\frac{155}{360}\times\pi\times18.49$.
$\frac{155}{360}\approx0.4306$, and $0.4306\times\pi\times18.49$.
Taking $\pi\approx3.14$, we have $0.4306\times3.14\times18.49$.
$0.4306\times3.14 = 1.3521$, and $1.3521\times18.49\approx25$.

Answer:

D. $25$ in$^{2}$