Question

A circular spinner has a radius of 6 inches. The spinner is divided into four sections of unequal area. The sector labeled green has a central angle of 120°. A point on the spinner is randomly selected.

What is the probability that the randomly selected point falls in the green sector?

A) 1/120
B) 1/12
C) 1/4
D) 1/3

Answer 1

1/120 is the correct answer

Answer 2

The area of the whole circle is πr², where r is the radius. In this case, the radius is 6 inches, so the area of the whole circle is 36π square inches.

The green sector has a central angle of 120°, which is one-third of the whole circle. Therefore, the area of the green sector is one-third of the area of the whole circle, or (1/3) × 36π = 12π square inches.

The probability of the randomly selected point falling in the green sector is equal to the ratio of the area of the green sector to the area of the whole circle. Therefore, the probability is:

(12π) / (36π) = 1/3

So the answer is D) 1/3