the face of a clock is divided into 12 equal parts. the radius of the clock face is 10 inches. assume the…

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.

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.

Answer

Answer:

B. The circumference of the clock is approximately 62.8 inches., C. The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°., E. The length of the minor arc between 6 and 7 is approximately 5.2 inches.

Explanation:

Step1: Calculate central - angle per part

The full - circle is 360°. Divided into 12 parts, so each part is $\frac{360^{\circ}}{12}=30^{\circ}$.

Step2: Calculate circumference

The formula for the circumference of a circle is $C = 2\pi r$. Given $r = 10$ inches, $C=2\times\pi\times10\approx2\times3.14\times10 = 62.8$ inches.

Step3: Calculate minor - arc measure from 12 to 4

There are 4 parts from 12 to 4. So the central angle (and arc measure) is $4\times30^{\circ}=120^{\circ}$.

Step4: Calculate major - arc length from 3 to 10

There are 7 parts from 3 to 10. The central angle is $7\times30^{\circ}=210^{\circ}$. The arc - length formula is $s=\theta r$ (where $\theta$ is in radians). First convert $210^{\circ}$ to radians: $210\times\frac{\pi}{180}=\frac{7\pi}{6}$. Then $s=\frac{7\pi}{6}\times10=\frac{70\pi}{6}\approx36.6$ inches.

Step5: Calculate minor - arc length from 6 to 7

There is 1 part from 6 to 7. The central angle is $30^{\circ}$, convert to radians: $30\times\frac{\pi}{180}=\frac{\pi}{6}$. Using the arc - length formula $s = \theta r$, with $r = 10$ inches, $s=\frac{\pi}{6}\times10=\frac{10\pi}{6}\approx5.2$ inches.