Calculate Height X of Rectangular Prism: Volume 45 cm³ with 2.5 cm × 4 cm Base

To solve this problem, we'll calculate the height $X$ of the rectangular prism using the given volume.

The volume of a rectangular prism is calculated using the formula:

$V = \text{length} \times \text{width} \times \text{height}$

We have the following values:

• Volume ($V$) = $45 \, \text{cm}^3$
• Length = $2.5 \, \text{cm}$
• Width = $4 \, \text{cm}$

Substitute these numbers into the volume formula and solve for $X$:

$45 = 2.5 \times 4 \times X$

First, calculate the product of the length and width:

$2.5 \times 4 = 10$

Substitute this back into the equation:

$45 = 10 \times X$

To isolate $X$, divide both sides by 10:

$X = \frac{45}{10} = 4.5$

Thus, the height $X$ of the rectangular prism is $4.5 \, \text{cm}$.