Volume of liquid in a tank

Water poured into a rectangular tank takes the shape of a cuboid, so nothing new is needed: `volume of water = length × width × depth of the water`. The two traps are both about reading. First, a part-filled tank gives you two vertical measurements — the tank's height and the water's depth — and only the water's depth belongs in the calculation. Second, the answer is usually wanted in litres: `1 ℓ = 1000 cm³`, so you **divide** cm³ by 1000 to get ℓ and multiply the other way. A sanity check that never fails: the number of litres must be smaller than the number of cm³.

Worked example

Problem A rectangular tank measures 40 cm by 20 cm by 30 cm. It contains water to a depth of 15 cm. Find the volume of water in ℓ, and the volume still needed to fill the tank.

Base of the tank: 40 × 20 = 800 cm². Every volume in this question is that base multiplied by a depth.
Water: 800 × 15 = 12000 cm³. Now 12000 ÷ 1000 = 12 ℓ.
The empty part is a cuboid too, 30 − 15 = 15 cm deep: 800 × 15 = 12000 cm³, so 12 ℓ more is needed.
Watch out The tank is 30 cm high, but the water reaches only 15 cm. Using 30 cm gives the tank's full capacity, not the water in it — this single misread costs more marks than any arithmetic slip in the topic.
Tip Check at the end: the water plus the top-up should equal the tank's full capacity, 800 × 30 = 24000 cm³ = 24 ℓ. It does.
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