Topics › Volume › Q139
Volume · filling time
P6 · Volume · PSLE Maths
Question
Mei Ling has a rectangular water tank with internal length, width and height of 60 cm, 45 cm and 50 cm respectively. The water is 18 cm deep at first. She turns on a tap that pours in 9 L of water every minute. How many minutes are needed to fill the tank to a depth of 42 cm? Take 1 L = 1000 cm³.
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Hint
First find the increase in water level, then find the volume of water added. Convert cm³ to L before dividing by the amount poured in each minute.
Show the answer and step-by-step explanation
Answer: Time needed 7.2 min
- See the levels — The base of the tank is 60 cm × 45 cm. The water rises from 18 cm deep to 42 cm deep.
- Find the rise — We only need to find the extra water added. The water level rises by 42 − 18 = 24 cm.
- Find volume added — Volume added = base area × rise in height. The base area is 60 × 45 = 2700 cm², so the volume added is 2700 × 24.
- Convert to litres — The tap rate is in L, so convert cm³ to L. Since 1 L = 1000 cm³, 64800 cm³ = 64.8 L.
- Divide by rate — The tap pours in 9 L every 1 minute. Time needed = 64.8 ÷ 9 = 7.2 min. 📌 Key idea: find the added volume in cm³, convert it to L, then use volume ÷ rate.
Method: For a rectangular tank, volume of water added = length × width × increase in water height. Convert cm³ to L, then use volume ÷ rate to find the time.
Practice: 3 similar questions
- Raju’s rectangular tank is 50 cm long, 40 cm wide and 35 cm high. The water is 12 cm deep at first, and he wants to fill it to a depth of 30 cm. The tap pours in 6 L every minute. How many minutes are needed? Take 1 L = 1000 cm³.
Answer
6 min — Rise in water level: 30 − 12 = 18 cm. Volume added: 50 × 40 × 18 = 36000 cm³. 36000 cm³ = 36 L. Time needed: 36 ÷ 6 = 6 min.
- A rectangular trough in the school garden is 80 cm long, 30 cm wide and 45 cm high. It is empty at first and is to be filled to a depth of 35 cm. The tap pours in 4.2 L every minute. How many minutes are needed? Take 1 L = 1000 cm³.
Answer
20 min — Volume added: 80 × 30 × 35 = 84000 cm³. 84000 cm³ = 84 L. Time needed: 84 ÷ 4.2 = 20 min.
- Siti’s rectangular tank is 75 cm long, 40 cm wide and 60 cm high. The water is 14 cm deep at first, and she wants to fill it to a depth of 50 cm. The tap pours in 9 L every minute. She has already left the tap on for 4 minutes. How many more minutes are needed? Take 1 L = 1000 cm³.
Answer
8 min — Total rise in water level: 50 − 14 = 36 cm. Total water needed: 75 × 40 × 36 = 108000 cm³ = 108 L. Water already poured in 4 minutes: 4 × 9 = 36 L. Remaining water: 108 − 36 = 72 L. More time needed: 72 ÷ 9 = 8 min.
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