Question

henry constructed circle a with a radius of 4 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. $\frac{315}{360}(4pi)$ b. $\frac{45}{360}(16pi)$ c. $\frac{315}{360}(16pi)$ d. $\frac{45}{360}(8pi)$

Explanation:

Step1: Recall area - of - circle formula

The area of a circle is $A = \pi r^{2}$. Given $r = 4$, then $A=\pi\times4^{2}=16\pi$.

Step2: Recall sector - area formula

The area of a sector of a circle with central angle $\theta$ (in degrees) is $A_{sector}=\frac{\theta}{360}\times A_{circle}$, where $\theta$ is the central - angle of the sector. Here, $\theta = 45^{\circ}$.

Step3: Calculate the area of the sector

Substitute $\theta = 45$ and $A_{circle}=16\pi$ into the sector - area formula. We get $A_{sector}=\frac{45}{360}(16\pi)$.

Answer:

B. $\frac{45}{360}(16\pi)$