the minute hand of a clock is 10.5 cm long. how far does the tip of the hand travel in 1 hour

The tip of the minute hand moves in a circle, so we need to find the circumference of that circle. The formula for the circumference of a circle is C = 2 * π * r, where r is the radius and C is the circumference.

In this case, the radius (r) is equal to the length of the minute hand, which is 10.5 cm.

C = 2 * π * 10.5 cm
C ≈ 2 * 3.14159 * 10.5 cm ≈ 65.97 cm

So the tip of the minute hand travels approximately 65.97 cm in 1 hour.