To find out how far the tip of the minute hand moves in 40 minutes, we need to calculate the distance it travels as it sweeps around the circle formed by the tip of the minute hand.
The formula to calculate the circumference of a circle is C = 2 * π * r, where r is the radius of the circle. In this case, the radius is the length of the minute hand, which is 15 cm.
So, we can calculate the circumference:
C = 2 * π * 15 cm
Plugging in the value of π (approximately 3.14), we get:
C ≈ 2 * 3.14 * 15 cm ≈ 94.2 cm
This means that in one complete revolution (which takes 60 minutes), the tip of the minute hand travels approximately 94.2 cm.
Now, to find out how far it moves in 40 minutes, we can set up a proportion. Since 40 minutes is two-thirds of 60 minutes, we calculate:
Distance moved = (40/60) * Circumference
This simplifies to:
Distance moved = (2/3) * 94.2 cm ≈ 62.8 cm
Therefore, the tip of the minute hand moves approximately 62.8 cm in 40 minutes.