Question

what is the area of the shaded sector? 190° 12 cm (not drawn to scale) a $\frac{19}{3}pi$ cm² b $144pi$ cm² c $76pi$ cm² d $\frac{25}{3}pi$ 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 values of $\theta$ and $r$

We are given that $\theta = 190^{\circ}$ and $r = 12\ cm$.

Step3: Substitute values into the formula

$A=\frac{190^{\circ}}{360^{\circ}}\times\pi\times(12)^{2}$.

Step4: Simplify the expression

First, $(12)^{2}=144$. Then $\frac{190}{360}\times144\pi$. $\frac{190\times144}{360}\pi=\frac{190\times144\div 20}{360\div 20}\pi=\frac{190\times7.2}{18}\pi$. $190\times7.2 = 1368$, and $\frac{1368}{18}=76$. So $A = 76\pi\ cm^{2}$.

Answer:

C. $76\pi\ cm^{2}$