What is the number of radians through which the minute hand (longer hand) of a clock rotates from 3:55 p.m. to 4:40 p.m. of the same day? (Enter an exact answer in terms of π.)

Answer 1

If we are only concern about the longer hand (minute hand) of the clock, then we can say:

3:55 PM to 4:55 PM => 360° or π radians

because it's one hour. So to answer the question, 3:55 pm to 4:40 pm is 15 minutes less than an hour, which is 45 minutes or 3 quarters of an hour. Therefore:

3:55 PM to 4:40 PM => (3/4)π radians

Answer 2

From 3:55 to 4:40 the "big" hand goes 45 minutes of a total of 60 minutes for one revolution.

That is it goes (3/4) of 2π=3π/2 radians.