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Volume · equal water levels
P6 · Volume · PSLE Maths
Question
Raju has two rectangular tanks on a level table. Tank A has a base of 48 cm × 25 cm and contains water to a depth of 35 cm. Tank B is empty and has a base of 60 cm × 30 cm. Raju pours water from Tank A into Tank B until the water levels in the two tanks are the same. No water is spilt. What is the height of the water in each tank then?
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Hint
Find the total volume of water first. When the levels are the same, each 1 cm rise uses the sum of the two base areas.
Show the answer and step-by-step explanation
Answer: common water height 14 cm
- Draw the situation — At first, only Tank A has water, with a depth of 35 cm. Tank B is empty.
- Find base areas — For each tank, every 1 cm rise needs water equal to its base area. Find the two base areas first.
- Combine 1 cm — Later the two water levels are the same. Imagine both water levels rising by 1 cm: it needs 1200 cm³ in A plus 1800 cm³ in B.
- Volume unchanged — Pouring the water does not change the total volume. At first, all the water is in A: 1200 × 35.
- Divide by sum — Common height = total volume ÷ water needed for each 1 cm rise. 42000 ÷ 3000 = 14.
- Check — Check: A has 1200 × 14 = 16800 cm³, and B has 1800 × 14 = 25200 cm³. The total is 42000 cm³, correct. 📌 Key idea: when the final water levels are the same, treat the tanks as one big base; divide the total volume by the sum of the base areas.
Method: The total volume of water remains unchanged. Common height = total volume of water ÷ sum of the base areas of the two tanks.
Practice: 3 similar questions
- Siti has two rectangular tanks. Tank A has a base of 45 cm × 20 cm and contains water to a depth of 20 cm. Tank B is empty and has a base of 30 cm × 20 cm. She pours water from A into B until the water levels are the same. What is the height of the water then?
Answer
12 cm — Base area of Tank A = 45 × 20 = 900 cm². Base area of Tank B = 30 × 20 = 600 cm². Original volume of water = 900 × 20 = 18000 cm³. Sum of base areas = 900 + 600 = 1500 cm². Common water height = 18000 ÷ 1500 = 12 cm.
- Mei Ling pours water from a rainwater tank into an empty planter box until the water levels in both containers are the same. The rainwater tank has a base of 48 cm × 20 cm and the water is 30 cm deep. The planter box has a base of 32 cm × 15 cm. What is the height of the water in both containers then?
Answer
20 cm — Base area of the rainwater tank = 48 × 20 = 960 cm². Base area of the planter box = 32 × 15 = 480 cm². Original volume of water = 960 × 30 = 28800 cm³. Sum of the two base areas = 960 + 480 = 1440 cm². Common water height = 28800 ÷ 1440 = 20 cm.
- Ali has two rectangular tanks. Tank A has a base of 60 cm × 25 cm and contains water to a depth of 28 cm. Tank B has a base of 45 cm × 20 cm and already contains water to a depth of 8 cm. Ali pours some water from A into B until the water levels in the two tanks are the same. What is the height of the water then?
Answer
20.5 cm — Base area of Tank A = 60 × 25 = 1500 cm², so its original water volume = 1500 × 28 = 42000 cm³. Base area of Tank B = 45 × 20 = 900 cm², so its original water volume = 900 × 8 = 7200 cm³. Total volume of water = 42000 + 7200 = 49200 cm³. Sum of the two base areas = 1500 + 900 = 2400 cm². Common water height = 49200 ÷ 2400 = 20.5 cm.
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