Answer:
The dimensions of the three possible boxes are;
Box 1: 2 inches length by 4 inches width by 5 inches height
Box 2: 2 inches length by 2 inches width by 10 inches height
Box 3: 8 inches length by 1 inch width by 5 inches height
Step-by-step explanation:
The dimensions of the required box = 40 in³
Therefore, a box that will hold all the cubes will have a dimension given as follows;
Length, l × Width, w × Height, h = 40 in.³
We therefore, look for possible dimensions of l, w, h, however to make is faster, we note that l × w = base area, BA, hence we look for the factors 40 thus;
BA × h ≡ l × w × h
8 × 5 = 40 ≡ 2 × 4 × 5 = 40
4 × 10 = 40 ≡ 2 × 2 × 10 = 40
8 × 5 = 40 ≡ 8 × 1 × 5 = 40
Hence we have our three possible boxes as follows;
Box 1: Length = 2 inches, width = 4 inches and height = 5 inches
Box 2: Length = 2 inches, width = 2 inches and height = 10 inches
Box 3: Length = 8 inches, width = 1 inches and height = 5 inches.
