Question

The circumference of the circle shown below is 54 centimeters. Which expression gives the length in centimeters of a 120° arc?

a) 360 / 120 * 54
b) 120 / 360 * 54
c) 360 * (120 / 360)
d) 54 / (360 / 120)

Answer 1

The length of a 120° arc in a circle with a 54 cm circumference is found by dividing the angle of the arc by the total angle in the circle and multiplying by the circumference, resulting in option b) 120 / 360 * 54.

Step-by-step explanation:

The student seeks to determine the length of a 120° arc in a circle with a circumference of 54 centimeters. To calculate an arc length, one must consider the proportion of the circle that the angle represents. Since there are 360 degrees in a full circle, a 120° arc is one-third of the circle. The correct expression is therefore the angle of the arc divided by the total angle of the circle, multiplied by its circumference.

b) 120 / 360 * 54 is the accurate option, which simplifies to (1/3) * 54, resulting in an arc length of 18 centimeters.