The volume of a cube is 2197 cm³. What is its lateral surface area (in cm²)?

Concept: For a cube of side length s, the volume is s3, the lateral surface area (the four vertical faces, excluding the top and bottom) is 4s2, and the total surface area (all six faces) is 6s2.

Application:

1. Find the side length from the given volume: s = ∛2197 cm = 13 cm, since 133 = 2197.

2. Apply the lateral surface area formula: LSA = 4 × 132 = 4 × 169 = 676 cm2.

Cross-check: 13 × 13 = 169 and 169 × 13 = 2197, confirming the side length is correct. The total surface area (all six faces) would instead be 6 × 169 = 1014 cm2, which is larger because it also includes the top and bottom faces — the question asks only for the lateral (side) surface area, which is 676 cm2.