When rotated about the 3 cm side, the height (h) is 3 cm and the radius (r) is 4 cm. The volume of the cone is $(1/3)πr^2h = (1/3)π(4^2)(3) = 16π~cm^3$. [The source answer key has 'c' which matches this calculation, but the solution calculates it as 12π].