Question

question 3 of 10 if the area of the circle below is 18 ft², what is the area of the shaded sector? a. 9 ft² b. 13.5 ft² c. 6 ft² d. 4.5 ft²

Explanation:

Step1: Recall sector - area formula

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 and $A_{circle}$ is the area of the whole circle.

Step2: Identify given values

We are given that $\theta = 90^{\circ}$ and $A_{circle}=18\ ft^{2}$.

Step3: Calculate the area of the sector

Substitute the values into the formula: $A_{sector}=\frac{90^{\circ}}{360^{\circ}}\times18$.
$A_{sector}=\frac{1}{4}\times18 = 4.5\ ft^{2}$.

Answer:

D. $4.5\ ft^{2}$