Calculate Cuboid Volume: 10cm Width with 40% and 50% Dimensional Relations

To solve this problem, we must calculate the missing dimensions of the cuboid and use the volume formula:

• Step 1: Determine the length of the cuboid.
• Step 2: Calculate the height of the cuboid.
• Step 3: Compute the volume using the cuboid's dimensions.

Let's work through each step in detail:

Step 1: Determine the Length.

The width of the cuboid is given as $10 \, \text{cm}$. The length is 40% less than the width. To find the length:

$\text{Length} = \text{Width} - 0.4 \times \text{Width}$

$\text{Length} = 10 - 0.4 \times 10 = 10 - 4 = 6 \, \text{cm}$

Step 2: Calculate the Height.

The height is 50% greater than the length. To find the height:

$\text{Height} = \text{Length} + 0.5 \times \text{Length}$

$\text{Height} = 6 + 0.5 \times 6 = 6 + 3 = 9 \, \text{cm}$

Step 3: Compute the Volume.

The volume of the cuboid is given by:

$V = \text{Length} \times \text{Width} \times \text{Height}$

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

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