Not exactly :)
If you try to print a 35cm x 40cm image on an A4 sheet, it would actually print a subsection of the image or re-size it. What you do need to know is the pixel density, which should be 72 pixels/inch for standard printing work. This means in every inch of your paper 72 pixels will be printed.
Now as a novice you may ask will cranking this value to say 300 pixels/inch increase the image quality? The answer is NO as far as printing is concerned as the details won't be visible.
However note that pixel density has zero effect on how your image appears on your screen, since your display has nothing to do with the printer you use.
A few good links to clear your concepts:
How Image Resolution Affects Print Quality
Image Resolution, Pixel Dimensions and Document Size in Photoshop
Hope I helped.