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Volume · rise in water level
P6 · Volume · PSLE Maths
Question
Mei Ling has a rectangular tank with a base measuring 50 cm by 32 cm. After she puts a stone completely into the water, the water level rises from 18 cm to 22.5 cm. Find the volume of the stone.
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Hint
The water displaced by the stone is exactly the volume of the rectangular layer by which the water rises.
Show the answer and step-by-step explanation
Answer: Volume of the stone 7200 cm³
- See the rise — When the stone is completely put into the water, it pushes the water up. The volume of the layer by which the water rises is the volume of the stone.
- Find the increase — The water level rises from 18 cm to 22.5 cm. The increase in height is 22.5 − 18 = 4.5 cm.
- Find base area — The risen layer of water is a thin cuboid. Its base is the same as the base of the tank: 50 cm × 32 cm.
- A thin cuboid — Look at the risen water alone: its base area is 1600 cm², and its height is 4.5 cm.
- Find volume — Volume of the stone = volume of the risen water. 1600 × 4.5 = 7200 cm³. 📌 Key idea: when an object is completely submerged, volume of object = base area of tank × rise in water level.
Method: Find the increase in water level first. Then use base area of the tank × increase in height to find the volume of the risen water; this is the volume of the stone.
Practice: 3 similar questions
- A rectangular tank has a base measuring 40 cm by 25 cm. After Raju puts a toy completely into the water, the water level rises from 12 cm to 15.5 cm. What is the volume of the toy?
Answer
3500 cm³ — Rise in water level: 15.5 − 12 = 3.5 cm. Base area of the tank: 40 × 25 = 1000 cm². Volume of the toy = 1000 × 3.5 = 3500 cm³.
- Siti's rectangular fish tank has a base measuring 60 cm by 30 cm. After she puts a decorative stone completely into the water, the water level rises by 2.8 cm. What is the volume of the decorative stone?
Answer
5040 cm³ — Base area of the fish tank: 60 × 30 = 1800 cm². Volume of the decorative stone = 1800 × 2.8 = 5040 cm³.
- Ali puts 3 identical stones completely into a rectangular tank. The base of the tank measures 45 cm by 28 cm, and the water level rises by 2.4 cm altogether. What is the volume of each stone?
Answer
1008 cm³ — Base area of the tank: 45 × 28 = 1260 cm². Total volume of the 3 stones = 1260 × 2.4 = 3024 cm³. Volume of each stone = 3024 ÷ 3 = 1008 cm³.
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