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Volume · change in water level
P6 · Volume · PSLE Maths
Question
Siti has a rectangular water tank with an internal length of 48 cm, breadth of 25 cm and height of 35 cm. The tank was 3/7 full at first. Siti poured in 7.2 L of water and then poured out 4.8 L of water. What is the height of the water now in cm?
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Hint
First find the original water height. Then convert the net increase in water from L to cm³ and use base area × change in height.
Show the answer and step-by-step explanation
Answer: Height of water now 17 cm
- Draw tank — First draw the cross-section and water level. The tank height is 35 cm, and it was 3/7 full at first.
- Find first height — 7 units are 35 cm, so 1 unit is 35 ÷ 7 = 5 cm. The water was 3 units high: 15 cm.
- Find net volume — Siti poured in 7.2 L and poured out 4.8 L, so the water increased by 2.4 L altogether. Remember: 1 L = 1000 cm³, so 2.4 L = 2400 cm³.
- Find the rise — The base area is 1200 cm². The extra 2400 cm³ of water spreads over the same base, so the water level rises by 2400 ÷ 1200 = 2 cm.
- Find final height — The water was 15 cm high at first and rose by 2 cm. The height of the water now is 17 cm. 📌 Key idea: convert units first, 1 L = 1000 cm³; change in water height = change in volume ÷ base area.
Method: In a rectangular tank, change in volume = base area × change in water height. So, change in height = change in volume ÷ base area. Convert L to cm³ first: 1 L = 1000 cm³.
Practice: 3 similar questions
- A rectangular water tank has an internal length of 40 cm, breadth of 30 cm and height of 28 cm. It was 1/2 full at first. Raju poured in 6 L of water and then poured out 3.6 L of water. What is the height of the water now in cm?
Answer
16 cm — Original water height = 28 × 1/2 = 14 cm. Base area = 40 × 30 = 1200 cm². Net increase in water = 6 L − 3.6 L = 2.4 L = 2400 cm³. Rise in water level = 2400 ÷ 1200 = 2 cm. Height of water now = 14 + 2 = 16 cm.
- A rectangular aquarium in school has an internal length of 50 cm, breadth of 20 cm and height of 30 cm. It was 2/5 full at first. Siti first poured out 4 L of water and then poured in 7 L of water. What is the height of the water now in cm?
Answer
15 cm — Original water height = 30 × 2/5 = 12 cm. Base area = 50 × 20 = 1000 cm². Net increase in water = 7 L − 4 L = 3 L = 3000 cm³. Rise in water level = 3000 ÷ 1000 = 3 cm. Height of water now = 12 + 3 = 15 cm.
- Mei Ling has a rectangular water tank with an internal length of 60 cm, breadth of 35 cm and height of 42 cm. It was 5/6 full at first. She poured out 12.6 L of water and then poured in 4.2 L of water. What is the height of the water now in cm?
Answer
31 cm — Original water height = 42 × 5/6 = 35 cm. Base area = 60 × 35 = 2100 cm². Net decrease in water = 12.6 L − 4.2 L = 8.4 L = 8400 cm³. Drop in water level = 8400 ÷ 2100 = 4 cm. Height of water now = 35 − 4 = 31 cm.
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