Leo+DadMade for Leo
Volume of a Prism
Rung 4 of 4 · Mastery

Prisms in the Real World

Fish tanks, shipping boxes, tents — they're all prisms. This is where capacity, litres, and running the formula backwards all pay off.


BuildDrag the tank to resize it. Then try the “reverse challenge”.
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"How much will it hold?" is just a volume question wearing everyday clothes. A fish tank, a shipping box, a triangular tent — find the end face, multiply by the length, and you've got the capacity.

Capacity, and Litres

The tank in the toy is a rectangular prism. Its glass end is the cross-section; the tank runs back along its length. Capacity = cross-section × length, exactly like before. The one new fact worth carrying around: 1000 cm³ = 1 litre. So a tank holding 60 000 cm³ holds 60 litres. That's how you go from "maths answer" to "how many buckets of water".

The bridge to real life: work out the volume in cm³, then divide by 1000 to get litres. Big tanks, fuel cans, water troughs — same trick.

Working Backwards

Often you know the capacity and need a missing measurement. A tank must hold 120 cm³ and its end face is fixed at 5 × 4 = 20 cm² — how long must it be? Start from Volume = cross-section × length: 120 = 20 × length, so length = 120 ÷ 20 = 6 cm. Multiplying built the volume; dividing undoes it. Flip on the reverse challenge in the toy and drag the length until the capacity hits the target — that's this exact move, felt in your hands.

Why This Is the Finish Line

Stacking cubes was the "aha". Cross-section × length made it quick. Picking the right face kept it safe. But sizing a real tank, converting to litres, and running the formula backwards to find a missing side — that's the bit that shows up when you're buying an aquarium, packing a removal van, or sitting an exam. That's mastery.

Us, Thinking Out Loud

How many litres would our kitchen sink hold, roughly?

The backwards one — how do we "undo" a multiply to find the missing length?

Of the four steps, which should we re-drag in a fortnight?