jmc

Rotating $△ABC$ around leg $\overline{CB}$ produces a cone with radius 3 cm, height 4 cm, and volume $$\frac{1}{3}\pi (3^2)(4)=12\pi$$ cubic cm.

Rotating $△ABC$ around leg $\overline{AB}$ produces a cone with radius 4 cm, height 3 cm, and volume $$\frac{1}{3}\pi (4^2)(3)=16\pi$$ cubic cm.

$16\pi \approx 50.27$ cubic cm is the greater volume. To the nearest whole number, this value is $\boxed{50}$ cubic cm.