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.
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.

Explanation:

Step1: Calculate per-section central angle

A full circle is $360^\circ$, divided into 12 parts.
$\text{Angle per section} = \frac{360^\circ}{12} = 30^\circ$

Step2: Verify Statement 1 (2 to 4)

2 sections apart: $2 \times 30^\circ = 60^\circ$

Step3: Verify Statement 2 (Circumference)

Circumference formula: $C=2\pi r$, $r=6$ in.
$C=2\pi(6)=12\pi \approx 37.7$ in

Step4: Verify Statement 3 (5 to 10 minor arc)

5 sections apart. Arc length: $s=\frac{\theta}{360^\circ} \times 2\pi r$, $\theta=5 \times 30^\circ=150^\circ$
$s=\frac{150^\circ}{360^\circ} \times 12\pi = 5\pi \approx 15.7$ in

Step5: Verify Statement 4 (1 to 9 minor arc)

Shorter distance is 4 sections: $4 \times 30^\circ=120^\circ$

Step6: Verify Statement 5 (11-2 vs 7-10)

11 to 2: 3 sections; 7 to 10: 3 sections. Equal arc lengths.

Answer:

• The central angle measure when one hand points at 2 and the other points at 4 is $60^\circ$.
• With one hand at 5 and the other at 10, the minor arc formed by the hands is about 15.7 in.
• The length of the minor arc between 11 and 2 is the same as the length of the minor arc between 7 and 10.