Question

The minute hand of a clock is 8 inches long. How far does the tip of the minute hand move in 30 minutes? How far does it move in 20 minutes?

Answer 1

Answer:

In 30 minutes:

The minute hand moves a distance of 25.13 inches

In 20 minutes:

The minute hand moves a distance of 16.76 inches

Step-by-step explanation:

When 60 minutes are completed, the minute hand of the relog makes a complete revolution. The distance s that the minute hand travels when making a complete revolution is:

$s = 2\pi r$ Where r is the radius of the circumference, and in this case, the radius of the minute hand.

So:

$s = 16 \pi$

s = 50.27 inches.

In 30 minutes (which is half of 60) the minute hand covers only half a revolution. Then the distance traveled in 30 minutes is $\frac{1}{2}(s) = 25.13$ inches

In 20 minutes (which is one third of 60) the minute hand only travels a third of a complete revolution. Then the distance traveled in 20 minutes is $\frac{1}{3}(s) = 16.76$ inches