A rectangular tank measuring 160 cm by 50 cm by 110 cm is 70% filled with water. 8 identical barrels of water that are completely filled are then scooped out from it. The water level drops to 40 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 10 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
= 110 x 70%
= 77 cm
Difference in height when 8 barrels were scooped out
= 77 - 40
= 37 cm
Volume of 8 barrels
= 160 x 50 x 37
= 296000 cm
3 Volume of 1 barrel
= 296000 ÷ 8
= 37000 mℓ
= 37 ℓ
(b)
Remaining water in the tank
= 160 x 50 x 40
= 320000 cm
3 50 ℓ = 50000 mℓ
Total volume of water to drain
= 320000 + 50000
= 370000 mℓ
10 ℓ = 10000 mℓ
Time taken to drain the water
= 370000 ÷ 10000
= 37 min
Answer(s): (a) 37 ℓ; (b) 37 min