Calculate Cuboid Volume: 4 Equal Orthohedra with AB=4 and BC=3/4AB

To solve the problem, let's determine the dimensions of the large cuboid:

• Step 1: Identify the given values: $AB = 4$, $BC = \frac{3}{4} \times AB$, and $BE = \frac{1}{2} \times AB$.
• Step 2: Calculate the dimensions of the cuboid:
• Since $AB = 4$, we find $BC = \frac{3}{4} \times 4 = 3$.
• Next, $BE = \frac{1}{2} \times 4 = 2$.
• Step 3: Calculate the volume of the large cuboid using the formula:
• $\text{Volume} = AB \times BC \times BE = 4 \times 3 \times 2 = 24$.
• Since the large cuboid is composed of four equal orthohedra, the volume of the entire large cuboid is $4 \times 24 = 96 \, \text{cm}^3$.

So, the volume of the large cuboid is $96 \, \text{cm}^3$.