Explanation:

- Start with the original formula for the volume of a cylinder: \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height.

- If the radius is increased by 150%, the new radius is \( 2.5r \).

- If the height is increased by 50%, the new height is \( 1.5h \).

- Compute the new volume: \( V_{new} = \pi (2.5r)^2 (1.5h) \).

- Simplify to get \( V_{new} = \pi \cdot 6.25r^2 \cdot 1.5h = 9.375 \pi r^2 h \).

- Compare with the original volume \( V = \pi r^2 h \).

- The new volume is \( 9.375 \) times the original, which means a 837.5% increase in volume.

- Option 4: 837.5% is correct.