Calculate Cuboid Volume: 12cm Width with 40% Length and 30% Height Proportions

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

• Step 1: Identify the given information and calculate the length and height.

• Step 2: Apply the formula for the volume of a cuboid.

• Step 3: Perform the necessary calculations to find the volume.

Now, let's work through each step:

Step 1: Identify the given information and calculate the dimensions

We know the cuboid has a width of $w = 12$ cm. The length $l$ is stated to be 40% of this width. Thus, we calculate:
$l = 0.4 \times 12 = 4.8$ cm.

The height $h$ is 30% of the width, so:
$h = 0.3 \times 12 = 3.6$ cm.

Step 2: Apply the formula for the volume of a cuboid

The formula for the volume of a cuboid is given by $V = l \times w \times h$.

Step 3: Calculate the volume

Now, substitute the values for $l$, $w$, and $h$:
$V = 4.8 \times 12 \times 3.6 = 207.36$ cm³.

Therefore, the volume of the cuboid is $207.36$ cm³.