A cube has volume 6240 cubic centimetres. How many rectangular boxes of internal dimensions 10 cm × 8 cm × 6 cm can fit in it by volume count (ignoring packing gaps)?

Introduction / Context:
Sometimes questions approximate capacity by comparing volumes, ignoring geometric packing constraints. Here, we are effectively asked how many smaller boxes of given internal volume would “fill” a larger cubic capacity of 6240 cm^3. The integer quotient provides the count when a perfect pack is not required in the statement.

Given Data / Assumptions:

• Large capacity (cube) V_big = 6240 cm^3.
• Each small box internal volume V_small = 10 * 8 * 6 = 480 cm^3.
• Interpretation: count by volume, i.e., floor(V_big / V_small).

Concept / Approach:
Divide total capacity by unit capacity: 6240 / 480. As the options are small integers, the result will be exact here.

Step-by-Step Solution:
V_small = 480 cm^3N = 6240 / 480 = 13

Verification / Alternative check:
13 * 480 = 6240 cm^3 exactly; thus the capacity-based count is an integer.

Why Other Options Are Wrong:
12 gives only 5760 cm^3, leaving unused capacity; 15 and 17 exceed the given capacity.

Common Pitfalls:
Confusing a capacity (volume) question with a strict geometric packing/tiling question requiring divisibility along each dimension. The wording here supports capacity-based counting.

Final Answer:
13