Geometry

Question Analysis:
This is a reverse volume problem where we know the number and volume of small objects packed inside, and must work backward to find a missing dimension of the prism.
The main focus is on forming and solving an equation involving volume and percentages.

Key Concept Explanation:
Total volume of foam = number of cubes × volume per cube
That volume equals 80% of the box’s full volume
Volume of prism = length × width × height
Solve for the unknown length x

Step-by-Step Solution:
Total foam volume = 480 × 5 = 2400 cm³
This represents 80% of the box's volume →
Full box volume = 2400 ÷ 0.8 = 3000 cm³
Use prism volume formula:
x × 15 × 10 = 3000