Step 1: Picture the two spillway types being compared: a free overfall (water drops off a crest into the air) versus a chute (water is guided down a lined channel that follows the ground slope).
Step 2: Statement (I) is simply the working definition of a chute spillway, so it holds.
Step 3: For economy, think about what a series of drop structures on a steep slope needs: multiple crest walls, multiple stilling basins, more material and labour. A single continuous chute avoids this repetition, so it costs less on steep terrain, confirming Statement (II).
Step 4: Since both descriptions agree with standard spillway engineering, neither statement is false.
\[\boxed{\text{Both Statement (I) and Statement (II) are correct}}\]