Question

question 8 of 10
a circle has an area of 30 in². what is the area of a 60° sector of this circle?
a. 3 in²
b. 6 in²
c. 5 in²
d. 10 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 know that $\theta = 60^{\circ}$ and $A_{circle}=30$ in². Substituting these values into the formula, we get $A_{sector}=\frac{60^{\circ}}{360^{\circ}}\times30$ in².

Step3: Simplify the expression

$\frac{60}{360}\times30=\frac{1}{6}\times30 = 5$ in².

Answer:

C. 5 in²