A rectangular tank has a base 40 cm long and 30 cm wide. It contains water to a depth of 15 cm. A solid stone shaped like a cuboid, 20 cm long, 10 cm wide and 12 cm high, is then placed fully inside the tank and is completely under the water.
- Find the volume of water in the tank at first, in litres. (1 litre = 1000 cm³)
- Find the height of the water in the tank after the stone is placed inside.
Need a hint?
For (a), multiply length, width and depth first, then convert cm³ to litres. For (b), the stone pushes water up by the volume it takes up, shared over the base area.
Worked answer
- (a) Volume of water = 40 × 30 × 15 = 18 000 cm³.
- (a) 18 000 cm³ ÷ 1000 = 18 litres.
- (b) Volume of stone = 20 × 10 × 12 = 2400 cm³.
- (b) Base area = 40 × 30 = 1200 cm², so the water rises by 2400 ÷ 1200 = 2 cm.
- (b) New height = 15 + 2 = 17 cm.
The mistake this question tests
Converting units (kg, ℓ, m, cm³)
Pupils often add the stone's height (12 cm) to the water depth instead of working out how far the water rises from the stone's volume, giving 27 cm.
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