Question

in circle l, a sector is shaded. ∠mln measures 120°. what fraction of the interior of the circle is shaded? simplify your answer. which expression represents the area of the shaded sector in square centimeters? \\(\frac{3}{16}(25\pi)\\) \\(\frac{3}{10}(100\pi)\\) \\(\frac{1}{3}(25\pi)\\) \\(\frac{1}{3}(100\pi)\\)

Explanation:

Step1: Find shaded fraction of circle

A full circle is $360^\circ$. The shaded sector has a central angle of $120^\circ$. The fraction is the ratio of the sector angle to the full circle angle.
$\text{Fraction} = \frac{120^\circ}{360^\circ} = \frac{1}{3}$

Step2: Calculate total area of circle

The radius $r = 10$ cm. The area of a circle is $A = \pi r^2$.
$A = \pi (10)^2 = 100\pi$

Step3: Find area of shaded sector

The area of the sector is the fraction of the circle times the total area.
$\text{Sector Area} = \frac{1}{3} \times 100\pi = \frac{1}{3}(100\pi)$

Answer:

Fraction of shaded circle: $\frac{1}{3}$
Correct area expression: $\frac{1}{3}(100\pi)$