Answer:
The six possible rectangular prisms Anabelle could build are;
W = 1, B = 1, L = 56
W = 1, B = 2, L = 28
W = 1, B = 4, L = 14
W = 2, B = 2, L = 14
W = 1, B = 7, L = 8
W = 2, B = 4, L = 7
Step-by-step explanation:
The number 1 cm³ Annabelle has = 56
The dimensions volume of the cubes Annabelle could build with the 1 cm³ = 56 cm³
The volume of rectangular prism, V = L × B × W
∴ For the rectangular prism, V = 56 cm³ = L × B × W
Therefore, the possible dimensions of the prism are three factors of 56, including;
1, 2, 4, 7, 8, 14, 28, 56
The combination of 3 factors of 56 that can be multiplied together to give 56 and therefore, the possible rectangular prisms includes;
W × L × B = A
1) 1 × 1 × 56 = 56
2) 1 × 2 × 28 = 56
3) 1 × 4 × 14 = 56
4) 2 × 2 × 14 = 56
5) 1 × 7 × 8 = 56
6) 2 × 4 × 7 = 56
There are therefore 6 possible rectangular prisms Annabelle could build
