Question

Quentin has 18 unit cubes. how many different rectangular prisms can be build if he uses unit cubes

Answer 1

18 = 2·3·3

So possibles prisms are:

2×3×3

1×2×9

1×6×3

1×1×18

Therefore Quentin can make 4 different rectangular prism with 18 unit cubes.

Answer 2

Quentin could built 3 different rectangular prism.

Explanation:

Quentin could built by arranging the unit cubes in rows and columns. Let us say R units cubes are in a row and C unit cubes in a column.

R × C = 18 = 1 × 2 × 3 × 6 × 9 × 18

1. R = 18 C = 1 This prism is same as if R = 1 and C = 18

2. R = 9 C = 2 same if R = 2, C = 9

3. R = 3 C = 6

So answer is 3.