Question

question 5 of 10 what is the approximate area of the shaded sector in the circle shown below? a. 11.78 cm² b. 5.89 cm² c. 26.5 cm² d. 53.0 cm²

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 $\theta = 150^{\circ}$ and $r = 4.5\ cm$.

Step3: Substitute values into the formula

$A=\frac{150^{\circ}}{360^{\circ}}\times\pi\times(4.5)^{2}$.
First, $\frac{150}{360}=\frac{5}{12}$, and $(4.5)^{2}=20.25$. So $A=\frac{5}{12}\times\pi\times20.25$.

Step4: Calculate the area

$A=\frac{5\times20.25\pi}{12}=\frac{101.25\pi}{12}$.
Taking $\pi\approx3.14$, we have $A=\frac{101.25\times3.14}{12}=\frac{317.625}{12}\approx26.47\approx26.5\ cm^{2}$.

Answer:

C. $26.5\ cm^{2}$