This assumes that you have a basic Kenmore / Whirlpool top load, direct drive, neutral drain (it doesn't spin until the pump removes most of the water) machine.
First, see the Sears parts site for your washer:
Enter your model number (###.######) and you'll see a list of major sub-components with diagrams and parts.
The numbers following the 110 (which means it's made by Whirlpool) are usually 8 digits. Using the number that you provided, I couldn't find your washer on the Sears site. You will want to verify the number (usually by lifting the lid) and/or check for manuals / parts site from the following Sears site:
Sears has replacement tubs (at least for my 12 year old top load for about $116.75 (U.S.) but you may be able to get one from Whirlpool for about the same cost. If you can get to the diagrams on the sears site. they often have "Manufacturer Authorized Substitutes) which are Whirlpool numbers.
FOR EXAMPLE, SEE THE SITE FOR OUR WASHER AND YOU'LL SEE EXAMPLES OF PARTS, DIAGRAMS AND COSTS.