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 5π/6 radians. What is the ratio of the area of the first sector to that of the second?

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Accepted Answer

1. Formula: area of a sector is $A=	frac{1}{2}r^2	heta$ with $	heta$ in radians.

2. Convert $150^\circ$ to radians: $150^\circ=\frac{150\pi}{180}=\frac{5\pi}{6}$.

3. The other sector already has angle $\frac{5\pi}{6}$ and both have the same radius $r=10$.

4. So both areas are equal. The ratio is $1:1$.

FINAL_ANSWER: b

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