Open Middle®
Directions: Using the digits 1 through 9, at most one time each, place a digit in each box to create two rectangular prisms where the larger one has the greatest possible volume and is double the volume of the other.
Hint
How can we find the volume of a rectangular prism?
What does it mean for one quantity to be double another’s?
What does it mean for one quantity to be double another’s?
Answer
The greatest possible volume found so far is 144 cubic units for the rectangular prism with the greater volume and 72 cubic units for the one with the lesser volume. Possible dimensions include:
2 x 8 x 9 for the greater volume and 4 x 3 x 6 for the lesser volume
8 x 6 x 3 for the greater volume and 2 x 4 x 9 for the lesser volume
2 x 8 x 9 for the greater volume and 4 x 3 x 6 for the lesser volume
8 x 6 x 3 for the greater volume and 2 x 4 x 9 for the lesser volume
Source: Joe Schwartz and Robert Kaplinsky
8, 5, 6 for the big one 4, 2, 3 for the smaller one