Question

The face of a clock is divided into 12 equal parts. The radius of the clock face is 6 inches. Assume the hands of the clock will form a central angle.

The face of a clock is divided into 12 equal parts.

Which statements about the clock are accurate? Check all that apply.

The central angle measure when one hand points at 2 and the other points at 4 is 60°.
The circumference of the clock is about 19 in.
With one hand at 5 and the other at 10, the minor arc formed by the hands is about 15.7 in.
The minor arc measure when one hand points at 1 and the other hand points at 9 is 150°.
The length of the minor arc between 11 and 2 is the same as the length of the minor arc between 7 and 10.

Answer 1

Correct answers: statements 1, 3, and 5 are accurate. Explanations:

1) True. Each hour mark is 30° (360°/12). From 2 to 4 is 2 steps → 2·30° = 60°.

2) False. Circumference = 2πr = 2π(6) = 12π ≈ 37.7 in, not 19 in.

3) True. From 5 to 10 is 5 steps → angle = 5·30° = 150°. Arc length = r·θ(rad) = 6·(150°·π/180) = 6·(5π/6) = 5π ≈ 15.7 in.

4) False. From 1 to 9 the minor separation is 4 steps (the shorter way) → 4·30° = 120°, not 150°.

5) True. 11 to 2 and 7 to 10 are each 3 steps → each subtend 3·30° = 90°, so their minor arc lengths are equal.