Question

what is the area of a sector formed by a central angle of π/3 radians in a circle with radius 6 cm?
a. 18π square cm
b. 6π square cm
c. 12π square cm
d. 3π square cm

which unit below is used to measure angles in circles?
a. inches
b. radians
c. meters
d. arcs

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector of a circle is \(A=\frac{1}{2}r^{2}\theta\), where \(r\) is the radius of the circle and \(\theta\) is the central angle in radians.

Step2: Substitute the given values into the formula

Given \(r = 6\space cm\) and \(\theta=\frac{\pi}{3}\).

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Radians are a standard unit for measuring angles in circles in mathematics. Degrees and radians are the two main units for angle - measurement in circular geometry. While inches and meters are units of length, and arcs are parts of a circle's circumference.

Answer:

b. \(6\pi\space square\space cm\)