We want to find the value of $X$ in the given situation.
We are told that the areas of three faces of a right, rectangular prism are $X \hspace{.6mm} \mathrm{cm}^2$, $32 \hspace{.6mm} \mathrm{cm}^2$, and $48 \hspace{.6mm} \mathrm{cm}^2$.
To find the volume of the prism, we need to determine the value of $X$.
The volume of a right, rectangular prism can be found by multiplying the lengths of its three dimensions.
Let's call the dimensions of the prism $a$, $b$, and $c$.
We are given that the areas of three faces are $X \hspace{.6mm} \mathrm{cm}^2$, $32 \hspace{.6mm} \mathrm{cm}^2$, and $48 \hspace{.6mm} \mathrm{cm}^2$.
The areas of the faces are equal to the product of two dimensions.
We can set up the following equations:
$ab = X$
$bc = 32$
$ac = 48$
To find the volume, we can multiply all three equations together:
$(ab)(bc)(ac) = X \cdot 32 \cdot 48$
$a^2 b^2 c^2 = 1536X$
Taking the square root of both sides of the equation, we get:
$abc = \sqrt{1536X}$
Now, we know that the volume of the prism is equal to $abc$.
Given that the volume is 192, we can set up the equation:
$192 = \sqrt{1536X}$
To solve for $X$, we can square both sides of the equation:
$192^2 = (\sqrt{1536X})^2$
$36864 = 1536X$
Dividing both sides of the equation by 1536, we find:
$X = 24$
The value of $X$ is 24.
The answer is: 24
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
The areas of three of the faces of a right, rectangular prism are X \hspace{.6mm} \mathrm{cm}^2$, $32 \hspace{.6mm} \mathrm{cm}^2$, and $48 \hspace{.6mm} \mathrm{cm}^2$. What is the volume of the prism, in cubic centimeters?
If we know the answer to the above question is 192, what is the value of unknown variable X?

### Answer:
