The words can't, cant sound the same but have different meanings and spellings. Why do can't, cant sound the same even though they are completely different words?
The answer is simple: can't, cant are homophones of the English language.
Contraction of cannot.
Angular deviation from a vertical or horizontal plane or surface; an inclination or slope.
A slanted or oblique surface.
A thrust or motion that tilts something.
The tilt caused by such a thrust or motion.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.