Question

the circumference of the circle is 12π cm. what is the area of the shaded sector? 160° (not drawn to scale) a 48π cm² b 16π cm² c 36π cm² d 24π cm²

Explanation:

Step1: Find the radius of the circle

The formula for the circumference of a circle is $C = 2\pi r$. Given $C=12\pi$, we have $2\pi r=12\pi$. Solving for $r$ by dividing both sides by $2\pi$, we get $r = 6$ cm.

Step2: Find the area of the whole - circle

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

Step3: Find the area of the shaded sector

The formula for the area of a sector of a circle is $A_{sector}=\frac{\theta}{360^{\circ}}\times A_{circle}$, where $\theta$ is the central - angle of the sector. Here, $\theta = 160^{\circ}$ and $A_{circle}=36\pi$ $cm^{2}$. So $A_{sector}=\frac{160^{\circ}}{360^{\circ}}\times36\pi=\frac{4}{9}\times36\pi = 16\pi$ $cm^{2}$.

Answer:

B. $16\pi$ $cm^{2}$