3. Volume: Filling 3D Space

Volume measures how much space a solid takes up — think of how much water fills a tank. It uses cubic units (\(\text{cm}^3\), \(\text{m}^3\)).

A powerful pattern: for any solid with the same cross-section all the way up (a box, a cylinder, a prism), volume = area of the base × height.
\[ \text{Box: } V = l \times w \times h, \qquad \text{Cylinder: } V = \pi r^2 h. \]
Example: a cylindrical can with radius \(3\,\text{cm}\) and height \(10\,\text{cm}\).
\[ V = \pi (3)^2 (10) = 90\pi \approx 282.7\,\text{cm}^3. \]

For a box \(4 \times 3 \times 2\): \(V = 4 \times 3 \times 2 = 24\,\text{cm}^3\).

💡 Tip: spot the base shape first (rectangle? circle?), find its area, then multiply by the height.