A rectangular tank measuring 160 cm by 50 cm by 120 cm is 70% filled with water. 12 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 30 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
= 120 x 70%
= 84 cm
Difference in height when 12 bottles were scooped out
= 84 - 48
= 36 cm
Volume of 12 bottles
= 160 x 50 x 36
= 288000 cm
3 Volume of 1 bottle
= 288000 ÷ 12
= 24000 mℓ
= 24 ℓ
(b)
Remaining water in the tank
= 160 x 50 x 48
= 384000 cm
3 30 ℓ = 30000 mℓ
Total volume of water to drain
= 384000 + 30000
= 414000 mℓ
10 ℓ = 10000 mℓ
Time taken to drain the water
= 414000 ÷ 10000
= 41.4 min
Answer(s): (a) 24 ℓ; (b) 41.4 min