Question

1. a sector of a circle is created from a central angle with a measure of 60°. if the diameter of the circle is 6 inches, what is the area of the sector?

a. 8π in²
b. 6π in²
c. 2π in²
d. 1.5π in²

Explanation:

Step1: Find circle radius

Radius $r = \frac{\text{Diameter}}{2} = \frac{6}{2} = 3$ inches

Step2: Calculate full circle area

Area of circle $A_{circle} = \pi r^2 = \pi (3)^2 = 9\pi$ in²

Step3: Find sector area ratio

Ratio = $\frac{\text{Central Angle}}{360^\circ} = \frac{60^\circ}{360^\circ} = \frac{1}{6}$

Step4: Compute sector area

$A_{sector} = A_{circle} \times \text{Ratio} = 9\pi \times \frac{1}{6} = 1.5\pi$ in²

Answer:

D. $1.5\pi$ in²