To find the height of the rectangular prism, we use the formula for the volume of a rectangular prism which is given by [tex]\( V = l \times w \times h \)[/tex]. Given the volume [tex]\( V = 15168 \, m^3 \)[/tex], we can rearrange the formula to solve for the height [tex]\( h \)[/tex].
We start by isolating [tex]\( h \)[/tex]:
[tex]\[
h = \frac{V}{l \times w}
\][/tex]
Next, we need values for the length [tex]\( l \)[/tex] and the width [tex]\( w \)[/tex]. For this example, let's assume the length [tex]\( l \)[/tex] is 28 meters and the width [tex]\( w \)[/tex] is 18 meters.
Now, we substitute these values into our equation:
[tex]\[
h = \frac{15168}{28 \times 18}
\][/tex]
First, calculate the denominator:
[tex]\[
28 \times 18 = 504
\][/tex]
Then, perform the division:
[tex]\[
h = \frac{15168}{504} = 30.095238095238095
\][/tex]
So, the height [tex]\( h \)[/tex] of the rectangular prism is approximately:
[tex]\[
h = 30.095238095238095 \, \text{meters}
\][/tex]
Thus, the height of the box is [tex]\(\boxed{30.095238095238095}\)[/tex] meters.
