I lost my sims 3 disk and i have already installed it on my computer is there anyway i could still play it?:\

One thing you could do is look for a no cd crack online. It should come in the form of a .exe file that you replace your old one with so that you no longer need the disc to boot it up although I am not sure how legal this is.

The only other option I can think of is to buy one of the expansion packs as once you have an expansion pack installed you can use that disc to load up sims 3 instead.