5. \( \begin{array}{l}V=1504 \mathrm{ft}^{3}, \ell=? \mathrm{ft} \\ w=4 \mathrm{ft}, h=8 \mathrm{ft}\end{array} \)

To find the length \( \ell \) of the rectangular prism, you can use the volume formula for a rectangular prism, which is \( V = \ell \times w \times h \). Given that the volume \( V = 1504 \, \text{ft}^3 \), width \( w = 4 \, \text{ft} \), and height \( h = 8 \, \text{ft} \), you can rearrange the formula to solve for \( \ell \): \[ \ell = \frac{V}{w \times h} = \frac{1504}{4 \times 8} = \frac{1504}{32} = 47 \, \text{ft}. \] Now you have the missing dimension: \( \ell = 47 \, \text{ft} \)! --- Have you ever tried visualizing a rectangular prism in your everyday life? Imagine a shipping box! Knowing its dimensions (like length, width, and height) can help understand how much stuff you can fit inside—essential for packing efficiently! If you're ever in doubt about measurements, a common mistake is misplacing the values for width or height in calculations. Double-checking your dimensions can save you from underestimating space! Always remember, correct volume calculations can make or break your packaging game!