A rectangular tank measuring 140 cm by 70 cm by 120 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 44 cm. The remaining amount of water in the tank is later poured into a container that contains 30 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 70%
= 84 cm
Difference in height when 8 barrels were scooped out
= 84 - 44
= 40 cm
Volume of 8 barrels
= 140 x 70 x 40
= 392000 cm
3 Volume of 1 barrel
= 392000 ÷ 8
= 49000 mℓ
= 49 ℓ
(b)
Remaining water in the tank
= 140 x 70 x 44
= 431200 cm
3 30 ℓ = 30000 mℓ
Total volume of water to drain
= 431200 + 30000
= 461200 mℓ
20 ℓ = 20000 mℓ
Time taken to drain the water
= 461200 ÷ 20000
= 23.06 min
Answer(s): (a) 49 ℓ; (b) 23.06 min