Calculate Cuboid Length: Volume 96 cm³ with 3:2 Ratio and Height 4 cm

To solve this problem, we need to find the length of the cuboid using its volume and given dimensions. Let's break this down:

• Step 1: Express the length and width using the ratio given. Let $l = 3x$ and $w = 2x$, where $x$ is a common factor.
• Step 2: Apply the formula for the volume of the cuboid, $V = l \times w \times h$. Given that $h = 4$ cm and $V = 96$ cm³, the equation becomes:

$96 = (3x) \times (2x) \times 4$

Now, simplify and solve for $x$ :

$96 = 24x^2$

Dividing both sides by 24 gives:

$x^2 = 4$

Taking the square root of both sides, we find:

$x = 2$

Thus, the length of the cuboid is:

$l = 3x = 3 \times 2 = 6 \text{ cm}$

Therefore, the solution to the problem is $6 \text{ cm}$.