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.
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.

Explanation:

Step1: Calculate per segment angle

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

Step2: Verify Statement 1

From 1 to 3 is 2 segments: $2\times30^\circ=60^\circ
eq30^\circ$. Incorrect.

Step3: Verify Statement 2

Circumference formula: $C=2\pi r$. Substitute $r=10$: $C=2\times\pi\times10=20\pi\approx62.8$ inches. Correct.

Step4: Verify Statement 3

From 12 to 4 is 4 segments: $4\times30^\circ=120^\circ$. Correct.

Step5: Verify Statement 4

Major arc from 3 to 10: total segments $12-5=7$. Arc length formula: $L=\frac{\theta}{360^\circ}\times2\pi r$. $\theta=7\times30^\circ=210^\circ$, so $L=\frac{210^\circ}{360^\circ}\times20\pi=\frac{35\pi}{3}\approx36.65$ inches $
eq31.4$. Incorrect.

Step6: Verify Statement 5

Minor arc from 6 to7 is 1 segment: $\theta=30^\circ$. Arc length: $L=\frac{30^\circ}{360^\circ}\times20\pi=\frac{5\pi}{3}\approx5.2$ inches. Correct.

Answer:

• 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 minor arc between 6 and 7 is approximately 5.2 inches.