One way to approach the problem is to use the formula for the circumference of a circle, which is C = 2πr, where r is the radius or half the diameter of the circle, and π is the constant ratio of the circumference to the diameter, approximately equal to 3.14.
Since the minute hand rotates around the center of the clock, its path traces a circle with a radius of 8 cm. If we assume that the minute hand moves uniformly, then the angle it covers in 15 minutes is 1/4 of a full revolution or 90 degrees (360 degrees divided by 4). Therefore, the distance it travels along the circle is 1/4 of the circumference or:
C/4 = (2πr)/4 = πr/2
Substituting r = 8 cm, we get:
π(8 cm)/2 = 4π cm
Using a calculator or an approximation of π as 3.14, we get:
4π cm ≈ 12.6 cm (rounded to the nearest tenth)
Therefore, the tip of a minute hand on a clock travels about 12.6 cm in 15 minutes.
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 or round your answer to the nearest tenth.
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