Painted cuboid cut into 1cm cubes

Evaluate each structural block statement independently [cite: 4438, 4439, 4491, 4492]:

Statement 1 tracks cubes with no paint, which forms the interior unexposed core block[cite: 4444, 4496]. Reduce each dimension of the cuboid by 2 cm to strip away the outer face layer: Core Volume = (7 - 2) × (5 - 2) × (3 - 2) = 5 × 3 × 1 = 15 cubes. [cite: 4444, 4496] Statement 1 is exactly correct .

Statement 2 tracks edge cubes with exactly two painted faces: one blue and one green[cite: 4445, 4497]. Examine the dimension mapping: Blue paint is on the 7 × 3 faces, and Green paint is on the 5 × 3 faces[cite: 4438, 4491]. These specific faces meet along the edges that share the dimension of 3 cm. A standard cuboid features exactly 4 parallel edges matching this orientation. The number of 2-faced cubes residing strictly along any edge of length L is calculated as (L - 2). For our 3 cm edge: 3 - 2 = 1 cube per edge. Total blue-green cubes = 4 edges × 1 cube/edge = 4 cubes. Since the statement asserts there are 6, Statement 2 is incorrect[cite: 4445, 4497, 4521].

Answer: (a).