Question

A wall clock is 12 inches in diameter. The clock has twelve equally spaced numbers. What is the distance around the edge of the clock from 8 to 12?
Answer
3π
4π
π
2π

Answer 1

so like 4 pi?

Answer 2

i dont get it

Answer 3

Louise, if you're still here I can post the correct solution

Answer 4

Revised Solution:

The distance from hour 8 to hour 12 covers one-third of the entire circle, which translates to four-twelveths if going by the our ratio since 8 is four units from twelve. We need to find the angle that spans from the 8th hour to the 12th hour which is four hours or 4/12. To do this, we set up the following proportion: \[\frac{4}{12} = \frac{\theta}{360} \] This proportion means that there exists an angle that is a portion of the entire circle that is equal to the span of four of twelve hours of the clock, and theta is that angle.

Next, we solve for theta by cross multiplying and simplifying: \[12\theta = 1440\]\[\theta = \frac{1440}{12}\]\[\theta = 120 ^{\circ}\]Next we use the proportion for finding the circumference of the portion of the circle that spans four of 12 hours of the circle from 8 to 12: And we set it up like so:\[\frac{\theta}{360} = \frac{x}{2 \pi r}\] where x is that distance of the arc that spans from the 8th hour to the twelth hour. We know that theta = 120°. So we substitute that in as well as r = 6, since the radius is half the diameter: \[\frac{120}{360} = \frac{x}{2 \pi (6)}\] Simplifying this, we get:
\[\frac{1}{3} = \frac{x}{12 \pi}\] Solving for x, we get \[x = 4 \pi\]

\[\text{Thus, the distance around the edge of the clock Between 8 and 12 is }\space 4 \pi \text{.}\]