Calculate the Volume: Finding Small Cuboid in a 10cm × 5cm × 8cm Structure

To solve this problem, we need to determine the volume of a small cuboid when given a total volume comprising four such cuboids.

First, let's establish the dimensions of the large cuboid. According to the problem:

• The length ($L$) of the large cuboid is $10 \, \text{cm}$.
• The width ($W$) is half the length, so $W = \frac{10}{2} = 5 \, \text{cm}$.
• The height ($H$) is $\frac{4}{5}$ of the length, so $H = \frac{4}{5} \times 10 = 8 \, \text{cm}$.

Next, calculate the volume of the large cuboid using the volume formula:

$\text{Volume of Large Cuboid} = L \times W \times H = 10 \, \text{cm} \times 5 \, \text{cm} \times 8 \, \text{cm} = 400 \, \text{cm}^3$

Since the large cuboid is composed of 4 identical smaller cuboids, the volume of each smaller cuboid is:

$\text{Volume of Small Cuboid} = \frac{\text{Volume of Large Cuboid}}{4} = \frac{400 \, \text{cm}^3}{4} = 100 \, \text{cm}^3$

Thus, the volume of one small cuboid is $100 \, \text{cm}^3$.