Question

question 6 of 40 henry constructed circle a with a radius of 6 units. he then created a sector as shown in the figure below. which of the following expressions would help him find the area of the shaded sector? a. $\frac{90}{360}(12pi)$ b. $\frac{270}{360}(6pi)$ c. $\frac{90}{360}(36pi)$

Explanation:

Step1: Recall area - of - circle formula

The area of a circle is $A = \pi r^{2}$. Given $r = 6$, so $A=\pi\times6^{2}=36\pi$.

Step2: Recall sector - area formula

The area of a sector of a circle with central angle $\theta$ (in degrees) is $A_{sector}=\frac{\theta}{360}\times A_{circle}$. Here $\theta = 90$, so $A_{sector}=\frac{90}{360}(36\pi)$.

Answer:

C. $\frac{90}{360}(36\pi)$