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Annabelle has 56 1 cm³ what are the dimensions of the rectangle Langer prism Annabelle could build with all the cubes

User Tim Schoch
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1 Answer

1 vote

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

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

User Aero Wang
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