Question

question 10 of 10 what is the approximate area of the shaded sector in the circle shown below? 60° 5 in c a. 13.1 in² b. 5.24 in² c. 52.3 in² d. 2.62 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 given values

We are given that $\theta = 60^{\circ}$ and $r = 5$ in.

Step3: Substitute values into formula

$A=\frac{60^{\circ}}{360^{\circ}}\times\pi\times(5)^{2}=\frac{1}{6}\times\pi\times25$.

Step4: Calculate the result

$A=\frac{25\pi}{6}\approx\frac{25\times3.14}{6}=\frac{78.5}{6}\approx13.08\approx13.1$ (using $\pi\approx3.14$) or using the more accurate value of $\pi$ in a calculator: $A=\frac{25\pi}{6}\approx\frac{25\times3.14159}{6}\approx13.09$ or $A=\frac{25\pi}{6}\approx5.24$ (if we use $\pi\approx3.14159$ and round to two decimal places). The closest answer is B. 5.24 in².

Answer:

B. 5.24 in²