A sector of a circle has a central angle of 60° and a radius of 8 cm. Another sector of the same circle has a central angle of 3 π radians. What is the ratio of the area of the first sector to the area of the second sector?
A. 2:3
B. 1:2
C. 1:1 (Correct answer)
D. 1:3
Correct Answer
Option C — 1:1
Detailed Solution & Explanation
The correct answer is 1:1.
Key Points
Convert the second angle to degrees: π/3 radians = 60°.
Both sectors then have a 60° central angle on the same circle (r = 8), so their areas are identical.
Sector area = (θ/360)·πr²; with equal θ and equal r, the ratio is 1:1.
The whole question hinges on the radian-to-degree conversion — π/3 = 60° — after which the two sectors are obviously the same size.