Question
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.
Show work
Show work
Answers
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.
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.