Pixel Dimensions and File Size

Can anybody please explain the relation between pixel dimensions and file size?
Being naive, (or straight-forward if you prefer) I had assumed that pixel dimensions wide times pix dimension high = file size. Wrong!
For instance a .JPG file 374 X 500 has a file size of 41,275 bytes. But 374 times 500 = 18,700 so the two are different issues.

Thanks Rich. It kind of sounds like you know something about this.
I see 1 pixel, and 24 bit color would make 24 bits at 8 bits to a byte, so there's the 3 bytes.
I selected a certain photo and used the APPLE i command to see if could find if it had 8 bit color or, whatever. That infomation was not on the info function, but it did say something about RGB color profile.
Is 8 bit color a near certain bet in most applications, or was that just for the sake of illustration?
I Googled 8 bit color and go to a Wikipedia Article
http://en.wikipedia.org/wiki/Color_depth
which explained a lot, but its more technical depth than what I'm prepared to deal with. The net net, as far as I can tell is that image size (before compression) is dimension times color depth in its native mode, but I suppose what the native mode is and what the displayed mode is could be separate issues?
I was under the impression that the compression in JPG formt files comes out, or is decompressed, when the photo is printed or displayed? No?

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