Through how many radians does the minute hand of a clock rotate from 12:40 p.m. to 1:30 p.m.

Answer 1

Another way to consider this is to consider that there are 50 minutes between 12:40 and 1:30 (20 minutes to the top of the hour at 1:00 and 30 minutes to 1:30).

(50 minutes)/(60 minutes) = 5/6 of an hour.

An hour is one time around the clock face and one time around a circle is 2π radians.

(2π)(5/6) = 10π/6 = 5π/3 radians

Answer 2

This is a great problem!

It can be helpful to draw out a clock face for this problem.

The first thing I would do would be to remember where the minute hand would be on a clock face at 12:40.

The minute hand would be pointing to the 8.

Then I would remember where the minute hand would be pointing at 1:30.

The minute hand would be pointing to 6

Now the minute hand would pass how many numbers to go from 12:40 (pointing to 8) to 1:30 (pointing to 6).

It would pass 10 numbers, or in otherworld would transfer 10/12 of a whole revolution.

The number of radians in a whole revolution, a circle, is 2*pi.

Therefore (10/12)*2*pi = (5/3)*pi radians