Question

question 2 of 10 a circle has an area of 30 in². what is the area of a 60 - sector of this circle? a. 6 in² b. 5 in² c. 10 in² d. 3 in²

Explanation:

Step1: Recall sector - area formula

The area of a sector of a circle is given by $A_{sector}=\frac{\theta}{360^{\circ}}\times A_{circle}$, where $\theta$ is the central - angle of the sector and $A_{circle}$ is the area of the circle.

Step2: Substitute given values

We are given that $\theta = 60^{\circ}$ and $A_{circle}=30\ in^{2}$. Substituting these values into the formula, we get $A_{sector}=\frac{60^{\circ}}{360^{\circ}}\times30$.

Step3: Simplify the expression

$\frac{60}{360}\times30=\frac{1}{6}\times30 = 5\ in^{2}$.

Answer:

B. $5\ in^{2}$