Question

the circle shown below has a diameter of 12 centimeters. what is the approximate area of the shaded sector? a. 102 cm² b. 390 cm² c. 226 cm² d. 97 cm² 310°

Explanation:

Step1: Find the radius

The diameter $d = 12$ cm, and the radius $r=\frac{d}{2}=\frac{12}{2}=6$ cm.

Step2: Find the area of the whole - circle

The formula for the area of a circle is $A=\pi r^{2}$. Substituting $r = 6$ cm, we get $A=\pi\times6^{2}=36\pi$ $cm^{2}$.

Step3: Find the central - angle of the shaded sector

The central - angle of the shaded sector $\theta=310^{\circ}$.

Step4: Find the area of the shaded sector

The formula for the area of a sector is $A_{sector}=\frac{\theta}{360^{\circ}}\times A_{circle}$. Substituting $\theta = 310^{\circ}$ and $A_{circle}=36\pi$ $cm^{2}$, we have $A_{sector}=\frac{310^{\circ}}{360^{\circ}}\times36\pi$. First, $\frac{310}{360}\times36 = 31\pi$. Using $\pi\approx3.14$, we get $A_{sector}\approx31\times3.14 = 97.34\approx97$ $cm^{2}$.

Answer:

D. $97$ $cm^{2}$