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A sector of a circle has a central angle of 150° and radius 10 cm. Another sector of the same circle has a central angle of \(\frac{5\pi}{6}\) radians. What is the ratio of the area of the first sector to that of the second?

1. 3: 4
2. 1: 1
3. 4: 5
4. 5: 6

Correct answer: 1: 1

Solution

The first angle is 150°. The second angle \(\frac{5\pi}{6}\) radians equals 150°. Since both sectors are from the same circle and have equal central angles, their areas are equal.

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