A rectangular tank measuring 160 cm by 50 cm by 120 cm is 50% filled with water. 6 identical containers of water that are completely filled are then scooped out from it. The water level drops to 45 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 30 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 6 containers were scooped out
= 60 - 45
= 15 cm
Volume of 6 containers
= 160 x 50 x 15
= 120000 cm
3 Volume of 1 container
= 120000 ÷ 6
= 20000 mℓ
= 20 ℓ
(b)
Remaining water in the tank
= 160 x 50 x 45
= 360000 cm
3 30 ℓ = 30000 mℓ
Total volume of water to drain
= 360000 + 30000
= 390000 mℓ
30 ℓ = 30000 mℓ
Time taken to drain the water
= 390000 ÷ 30000
= 13 min
Answer(s): (a) 20 ℓ; (b) 13 min