Volume of Rectangular Prisms

Directions: Using the digits 1 through 9 at most one time each, fill in the boxes to create a rectangular prism with a volume that is greater than 100 cubic units. What’s the least volume? What’s the greatest volume?

Hint

How might starting at the least (or greatest) dimension/factor help you think about this problem?

Answer

There are several possibilities.
• 4 x 6 x 8 = 192
• 3 x 8 x 9 = 216
• 6 x 8 x 9 = 432

Source: Kari Frazier

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5 comments

  1. Greatest=504 units cubed
    Least=120 units cubed

  2. Rudolf Österreicher

    Greatest volume: 9 * 8 * 6 = 432
    Least volume: 4 * 6 * 8 = 192

    All possible solutions:
    3 * 8 * 9 = 216
    3 * 9 * 8 = 216
    4 * 6 * 8 = 192
    4 * 8 * 6 = 192
    6 * 4 * 8 = 192
    6 * 8 * 4 = 192
    6 * 8 * 9 = 432
    6 * 9 * 8 = 432
    8 * 3 * 9 = 216
    8 * 4 * 6 = 192
    8 * 6 * 4 = 192
    8 * 6 * 9 = 432
    8 * 9 * 3 = 216
    8 * 9 * 6 = 432
    9 * 3 * 8 = 216
    9 * 6 * 8 = 432
    9 * 8 * 3 = 216
    9 * 8 * 6 = 432

    • Why didn’t you use 9*8*7?? it would have given you 504 as the largest volume. and 9*6*2 would have given you a least volume of 108

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