Calculate Cuboid Volume: Width 10cm with 40% and 50% Proportional Dimensions

To solve this problem of finding the volume of the given cuboid, we will follow these detailed steps:

First, we need to calculate the length of the cuboid:

• The width is given as $10 \, \text{cm}$.
• The length is $40\%$ smaller than the width, so we calculate the change as $0.40 \times 10 \, \text{cm} = 4 \, \text{cm}$.
• Thus, the length is $10 \, \text{cm} - 4 \, \text{cm} = 6 \, \text{cm}$.

Next, we calculate the height of the cuboid:

• The height is $50\%$ of the length.
• Thus, the height is $0.50 \times 6 \, \text{cm} = 3 \, \text{cm}$.

Finally, calculate the volume of the cuboid using the formula:

• The volume $V$ is given by $V = \text{length} \times \text{width} \times \text{height}$.
• Substitute the known values: $V = 6 \, \text{cm} \times 10 \, \text{cm} \times 3 \, \text{cm}$.
• Perform the multiplication: $V = 180 \, \text{cm}^3$.

Therefore, the volume of the cuboid is $180 \, \text{cm}^3$.