SAT Circles Practice Question 4 (Medium)

Math · Geometry and TrigonometryMedium

A circle has a radius of $6$ centimeters. What is the area, in square centimeters, of a sector of the circle with a central angle of $150^\circ$ ?

$5\pi$

$15\pi$

$30\pi$

$36\pi$

Show answer and explanation

Answer: B

The sector is $\frac{150}{360} = \frac{5}{12}$ of the circle. The full circle's area is $\pi(6)^2 = 36\pi$ . So the sector's area is $\frac{5}{12} \cdot 36\pi = 15\pi$ .

Choice A is the length of the arc, $\frac{5}{12} \cdot 2\pi(6)$ , not the area of the sector.

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