Question

The face of a clock is divided into 12 equal parts. The radius of the clock face is 10 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? Select three options.

The central angle formed when one hand points at 1 and the other hand points at 3 is 30°.
The circumference of the clock is approximately 62.8 inches.
The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°.
The length of the major arc between 3 and 10 is approximately 31.4 inches.
The length of the minor arc between 6 and 7 is approximately 5.2 inches.

Answer 1

Correct choices: statements 2, 3, and 5.

Brief reasons:
- Circumference = 2πr = 2π(10) = 20π ≈ 62.8 — true.
- From 12 to 4 is 4 divisions; central (minor arc) angle = 4·30° = 120° — true.
- From 6 to 7 is 1 division; arc length = r·θ = 10·(30° in radians = π/6) = 10·π/6 = 5π/3 ≈ 5.24 ≈ 5.2 — true.

(1 is false: 1 to 3 is 2·30° = 60°. 4 is false: major arc 3 to 10 is 7·30° = 210°, length = 10·(210° in radians) ≈ 36.65, not 31.4.)