A rectangular tank measuring 150 cm by 50 cm by 100 cm is 50% filled with water. 15 identical bottles of water that are completely filled are then scooped out from it. The water level drops to 48 cm. The remaining amount of water in the tank is later poured into a container that contains 50 litres of water. The water is then drained out through a tap found at the bottom of the container at 20 litres per minute.
- What is the capacity of each pail? Answer in litres.
- How long did it take to drain the water from the container completely? Answer in terms of min.
(a)
Original height of water in the tank
= 100 x 50%
= 50 cm
Difference in height when 15 bottles were scooped out
= 50 - 48
= 2 cm
Volume of 15 bottles
= 150 x 50 x 2
= 15000 cm
3 Volume of 1 bottle
= 15000 ÷ 15
= 1000 mℓ
= 1 ℓ
(b)
Remaining water in the tank
= 150 x 50 x 48
= 360000 cm
3 50 ℓ = 50000 mℓ
Total volume of water to drain
= 360000 + 50000
= 410000 mℓ
20 ℓ = 20000 mℓ
Time taken to drain the water
= 410000 ÷ 20000
= 20.5 min
Answer(s): (a) 1 ℓ; (b) 20.5 min