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Volume of a Prism
Rung 1 of 4 · Discover

Where the Volume Formula Comes From

Spoiler: it's just area, repeated. Work out one slice, then count how many identical slices stack up along the length.

NESA MA4-VOL-C-01Builds on area

PlayAdd layers one at a time, or hit “fill it up”. Watch the cube count match cross-section × length.
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Audio WalkthroughComing Soon
Video ExplainerComing Soon

Volume answers one simple question: how many unit cubes fit inside the solid? A "unit cube" is just a 1 × 1 × 1 block — one centimetre each way, say. Count the cubes and you've got the volume.

One Slice, Copied Over and Over

A prism is special because it's the same shape the whole way through. So picture the flat end face — the cross-section — and tile it with unit squares. In the toy, that end holds 12 unit squares, so one layer of cubes sitting on it is 12 cubes. Now here's the lovely bit: every layer along the length is identical. Stack a layer for each unit of length and you're just adding the same 12 again and again. Five layers? 12 + 12 + 12 + 12 + 12 = 60 cubes. Press "fill it up" and watch them stack.

Say it plainly: volume = cubes in one layer × number of layers = area of the cross-section × length. The length just tells you how many copies of that end face to pile up.

So the "formula" Is Really Common Sense

People write it as Volume = cross-section area × length. It looks like a new rule to learn, but you've just seen it's only "find one slice, then count the slices". That's why it works for any prism — a box, a triangular tent, a hexagonal pencil — the end face can be any shape at all, and the recipe never changes.

Why "cubic" Units

Because you're counting cubes. If the sides are in centimetres, each little block is one cubic centimetre, so the answer is in cm³. The area of the end face was already in square units (cm²), and multiplying by a length (cm) adds the third dimension — that's the little ³ doing its job.

Us, Thinking Out Loud

Why does adding the same layer over and over turn into a multiplication?

What's a prism around the house we could "slice" into identical layers?