Question

what is the correct proportion to use to solve for the sector area?
11 ft
150°
○ a. $\frac{x}{3.14cdot11^{2}}=\frac{150}{360}$
○ b. $\frac{x}{2cdot3.14cdot11}=\frac{150}{360}$
○ c. $\frac{x}{3.14cdot11^{2}}=\frac{360}{150}$
○ d. $\frac{x}{3.14cdot11^{2}}=\frac{11}{360}$

Explanation:

Step1: Recall sector - area formula concept

The ratio of the area of a sector ($x$) to the area of the whole circle ($A=\pi r^{2}$) is equal to the ratio of the central - angle of the sector ($\theta$) to the total angle of a circle ($360^{\circ}$). Here, $r = 11$ ft and $\theta=150^{\circ}$, and the area of the whole circle is $A = 3.14\times11^{2}$.

Step2: Set up the proportion

The proportion is $\frac{x}{3.14\times11^{2}}=\frac{150}{360}$.

Answer:

A. $\frac{x}{3.14\times11^{2}}=\frac{150}{360}$