1. a. Through how many radians does the minute hand of a clock sweep between 9:05pm and 9:30pm?
b. The dial of Big Ben's clock in London is 23 feet in diameter. How long is the arch traced by the minute hand between 9:05pm and 9:30pm?

a

By revolving 60 minutes minute hand covers 2*pie radians

1 minutes covers = 2*pie/60 = pie/ 30 radians
25 minutes covers = pie*25/30 = 5*pie/6 radians

b

by covering 60 minutes arc covered 2*pie*23 =46*pie
1 degree cover = 46*pie/60
25 pie covers = 46*pie*25/60 radians

Hope this helps