Calculate Cuboid Volume: 10cm Width with 40% and 150% Proportional Dimensions

To solve this problem, we'll follow these steps:

• Step 1: Determine the length of the cuboid as a percentage of the width.
• Step 2: Calculate the height of the cuboid as a percentage increase from the length.
• Step 3: Use the dimensions to calculate the volume of the cuboid.

Now, let's work through each step:

Step 1: Calculate the length:

$L = W \times (1 - 0.40) = 10 \, \text{cm} \times 0.60 = 6 \, \text{cm}$

Step 2: Calculate the height:

$H = L \times 1.50 = 6 \, \text{cm} \times 1.50 = 9 \, \text{cm}$

Step 3: Calculate the volume:

$V = W \times L \times H = 10 \, \text{cm} \times 6 \, \text{cm} \times 9 \, \text{cm} = 540 \, \text{cm}^3$

Therefore, the volume of the cuboid is $\mathbf{540 \, \text{cm}^3}$.