A rectangular tank measuring 140 cm by 50 cm by 120 cm is 50% filled with water. 14 identical containers of water that are completely filled are then scooped out from it. The water level drops to 44 cm. The remaining amount of water in the tank is later poured into a container that contains 40 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
= 120 x 50%
= 60 cm
Difference in height when 14 containers were scooped out
= 60 - 44
= 16 cm
Volume of 14 containers
= 140 x 50 x 16
= 112000 cm
3 Volume of 1 container
= 112000 ÷ 14
= 8000 mℓ
= 8 ℓ
(b)
Remaining water in the tank
= 140 x 50 x 44
= 308000 cm
3 40 ℓ = 40000 mℓ
Total volume of water to drain
= 308000 + 40000
= 348000 mℓ
20 ℓ = 20000 mℓ
Time taken to drain the water
= 348000 ÷ 20000
= 17.4 min
Answer(s): (a) 8 ℓ; (b) 17.4 min