Welcome to the solids. So far you've measured flat shapes; this chapter measures what they can HOLD. Volume is counted in cubes — a box 4 m long, 3 m wide and 2 m tall holds 4 × 3 × 2 = 24 metre-cubes of space. That's the whole formula: $V = lwh$ (read aloud: V equals l times w times h) — $V$ the volume, in cubic units, and $l$, $w$, $h$ the box's length, width and height. A cube says it even faster: every edge matches, so with $a$ as that one edge, $V = a^3$ — a cubed, which just means a × a × a.

And here's the secret that unlocks the whole chapter: every prism is a STACK. Take the end face, find its area, and slide it along the length: $V = BL$ — base area times length, with $B$ the area of that end face and $L$ the length it runs. A triangular prism (picture a tent) stacks a triangle: $V = \tfrac{1}{2}\,b\,h\,L$, where $b$ and $h$ are the end triangle's base and height and the triangle's own half is built right in. Four formulas, one idea — the base does the talking, the length does the walking.