Question

Circle L is shown. Line segments K L and M L are radii. The length of K L is 12. Angle M L K is 60 degrees. Sector M L K with a 60 degree angle is shaded.
What is the area of the sector that is not shaded?

12Pi units squared
24Pi units squared
120Pi units squared

Answer 1

The area of the unshaded region of the circle will be 120π units squared.

The area of a sector of a circle of radius r having an angle a° is given by:

Area of sector = (π*$r^{2}$)*(a°/360°) units squared.

Given ∡KLM = 60°. The radius of the circle is 12 units.

⇒The area of shaded sector KLM =  (π*$12^{2}$)*(60°/360°) = π·144/6 = 24π sq. units.

The area of the unshaded region of the circle = (total area of the circle) - (the area of sector KLM) = (π*$12^{2}$) - 24π = 120π sq units.

∴ The area of the unshaded region of the circle is 120π units squared.

Learn more about area of sector here:

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