Question

The hour, minute, and second hands on a clock are 0.25 m , 0.31 m , and 0.34 m long, respectively.

Answer 1

In 1 hour, the hour hand sweeps across 1/12 of the clock's face. In 40 min, the hour hand travels (40 min)/(60 min) = 2/3 of the path it covers in an hour, so a total of 1/12 × 2/3 = 1/18 of the clock's face. This hand traces out a circle with radius 0.25 m, so in 40 min its tip traces out 1/18 of this circle's radius, or

1/18 × 2π (0.25 m) ≈ 0.087 m

The minute hand traverses (40 min)/(60 min) = 2/3 of the clock's face, so it traces out 2/3 of the circumference of a circle with radius 0.31 m:

2/3 × 2π (0.31 m) ≈ 1.3 m

The second hand completes 1 revolution each minute, so in 40 min it would fully trace the circumference of a circle with radius 0.34 m a total of 40 times, so it covers a distance of

40 × 2π (0.34 m) ≈ 85 m