The minute hand of a clock is 5 inches long. What distance does its tip move in 20 minutes?

Question

This is a precalculus question.

Answer 1

Assuming that the clock is circular, the length of the minute hand is the radius.

 

The distance that the tip of the minute hand moves in a given time is the length of an arc along the circle.  

 

If s is the length of arc, then s = rθ, where r is the radius and θ is the measure (in radians) of the central angle formed by the initial position and the final position of the minute hand (measured clockwise).  

 

r = 5"

20 minutes is 1/3 of an hour.

 

Since there are 2π radians in 1 rotation of the minute hand (1 hour),

θ = (1/3)(2π) = 2π/3.

 

So, s = rθ = (5")(2π/3) = 10π/3 inches ≈ 10.47"

 

 

Answer 2

20 minutes is 1/3 of a revolution (circumference).

The circumference is 10π.

 

10π / 3

 

Transform into units as directed.