How far does the tip of a minute hand on a clock travel in 15 minutes if the distance from the center to the tip is 8 cm? Leave your answer in terms of π or round your answer to the nearest tenth.
(This is tenth grade math, please don't make it advanced.)
Show work.
The minute hand travels in a circle with a radius of 8 cm. The circumference of a circle is given by the formula 2πr, where r is the radius. Therefore, the circumference of the circle that the minute hand travels in is:
2π(8 cm) = 16π cm
Since the minute hand travels the entire circumference in one hour (or 60 minutes), the distance it travels in 15 minutes is one-fourth of the circumference:
16π cm / 4 = 4π cm
Therefore, the tip of the minute hand travels 4π cm in 15 minutes. This can be rounded to the nearest tenth as approximately 12.6 cm.