Use the Volume formula, \( v \) 4. \( \begin{array}{l}V=75 \mathrm{~m}^{3}, \ell=5 \mathrm{~m} \\ w=5 \mathrm{~m}, h=? \mathrm{~m}\end{array} \)

To find the height \( h \) of the volume, we can use the formula for volume of a rectangular prism: \( V = \ell \times w \times h \). Given that \( V = 75 \, \mathrm{m}^3 \), \( \ell = 5 \, \mathrm{m} \), and \( w = 5 \, \mathrm{m} \), we can rearrange the formula to solve for \( h \): \[ h = \frac{V}{\ell \times w} = \frac{75 \, \mathrm{m}^3}{5 \, \mathrm{m} \times 5 \, \mathrm{m}} = \frac{75}{25} = 3 \, \mathrm{m}.\] So, the height \( h \) is \( 3 \, \mathrm{m} \). Did you know that the concept of volume dates back to ancient civilizations? The Egyptians, for example, had a solid understanding of area and volume, using it for agriculture and construction. They even developed methods to calculate the volume of objects and ensure their constructions were stable! If you're doing volume calculations often, watch out for common mix-ups! It's easy to confuse the dimensions when you’re juggling multiple figures. Always double-check your units and conversions, especially when switching from metric to imperial. Using a consistent unit system can save you from those pesky calculation errors!