Question

question 4 of 10 what is the approximate area of the shaded sector in the circle shown below? 180° 4.3 in a. 6.75 in² b. 13.51 in² c. 7.26 in² d. 29.04 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 figure, the radius $r = 4.3$ inches and the central - angle $\theta=180^{\circ}$.

Step3: Substitute values into formula

$A=\frac{180^{\circ}}{360^{\circ}}\times\pi\times(4.3)^{2}$.
Since $\frac{180^{\circ}}{360^{\circ}}=\frac{1}{2}$, we have $A=\frac{1}{2}\times\pi\times(4.3)^{2}$.

Step4: Calculate

First, $(4.3)^{2}=18.49$. Then $A=\frac{1}{2}\times\pi\times18.49$.
Taking $\pi\approx3.14$, we get $A=\frac{1}{2}\times3.14\times18.49 = 1.57\times18.49\approx13.51$ square inches.

Answer:

B. $13.51\text{ in}^2$