If the power company sells electrical energy at $.11 per kilowatt how much does it cost to run a 100 w radio for three hours

The power company sells energy.  But "kilowatt" is not energy.  It's a RATE of using energy.  

Take a close look at your electric bill. The power company charges       $0.11 per "kilowatt-hour".  That's the energy you use in 1 hour if you're taking it at the rate of 1 kilowatt.

Remember that 1 watt means 1 Joule of energy per second.

So 1 kilowatt = 1,000 Joules per second, and

1 kilowatt-hour = (1,000 J/sec) x (3,600 sec/hr) = 3,600,000 J

= = = = =

Now for your radio . . .

(3 hours) x (3,600 seconds/hour) = 10,800 seconds

100 watts = 100 Joules/second

Energy used = (100 J/sec) x (10,800 sec) = 1,080,000 Joules

(1,080,000 J) x (1 kilowatt-hour/3,600,000 J) = 0.3 kilowatt-hour

(0.3 kilowatt-hour) x (11¢/kilowatt-hour) = 3.3¢  <==

= = = = =

Slightly different way:

(100 watts) x (3 hours) = 300 watt-hour

"kilo ..." means "1,000" of something, so

300 watt-hours = 0.3 kilowatt-hour

Cost = (11¢/kilowatt-hour) x (0.3 kilowatt-hour) = 3.3¢