Understanding volume & nets
For a rectangular box (prism), volume = length × width × height. A net is the flat, unfolded version of a solid — fold it up and it becomes the box; this helps you see all the faces (which is also how you'd find surface area).
Seeing it in action
Worked example
A box is 2 by 3 by 4. Find its volume.
Volume = 2 × 3 × 4 = 24 cubic units.
Six faces: two 4×3, two 4×2 and two 2×3. Fold the net and it closes into the 2 × 3 × 4 box, whose volume is 2 × 3 × 4 = 24 cubic units.
A common mistake, and the fix
Adding the edges instead of multiplying them, or mixing up volume and surface area.
For a 2 by 3 by 4 box, 2 + 3 + 4 = 9 is not the volume; 2 × 3 × 4 = 24 cubic units is. The net shows the other measure: the faces of the net add up to the surface area, 2 × (6 + 8 + 12) = 52 square units, which is a different thing from the 24 cubes that fill the box.
Try a few
Box 5 by 2 by 3 — volume?
5 × 2 × 3.
Cube with side 3 — volume?
Box 1 by 4 by 6 — volume?
1 × 4 × 6.
How many faces does the net of a 2 by 3 by 4 box have?
two 2×3, two 2×4 and two 3×4 rectangles.
More geometry reasoning in Numeris.
Numeris doesn't have a star for volume & nets yet, but its geometry reasoning constellation practises the skills around it.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
Free printable · 3 pagesText version (screen-reader friendly): Draw it. Explain it. Math sample
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