Question

question 6 of 10 what is the approximate area of the shaded sector in the circle shown below? 14 in 30° c a. 3.67 in² b. 205 in² c. 7.33 in² d. 51 in²

Explanation:

Step1: Recall area - of - circle formula

The area of a full - circle is given by $A = \pi r^{2}$, where $r$ is the radius of the circle. Here, $r = 14$ inches, so $A=\pi\times(14)^{2}=196\pi\ in^{2}$.

Step2: Find the fraction of the circle represented by the sector

The central angle of the sector is $\theta = 30^{\circ}$. The total number of degrees in a circle is $360^{\circ}$. The fraction of the circle that the sector represents is $\frac{\theta}{360}=\frac{30}{360}=\frac{1}{12}$.

Step3: Calculate the area of the sector

The area of the sector $A_{s}$ is the fraction of the circle times the area of the full - circle. So $A_{s}=\frac{1}{12}\times196\pi$.
\[

$$\begin{align*} A_{s}&=\frac{196\pi}{12}\\ &=\frac{49\pi}{3}\\ &\approx\frac{49\times3.14}{3}\\ &=\frac{153.86}{3}\\ &\approx7.33\ in^{2} \end{align*}$$

\]

Answer:

C. $7.33\ in^{2}$