A rectangular tank measuring 140 cm by 70 cm by 130 cm is 60% filled with water. 7 identical bottles of water that are completely filled are then scooped out from it. The water level drops to 43 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 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
= 130 x 60%
= 78 cm
Difference in height when 7 bottles were scooped out
= 78 - 43
= 35 cm
Volume of 7 bottles
= 140 x 70 x 35
= 343000 cm
3 Volume of 1 bottle
= 343000 ÷ 7
= 49000 mℓ
= 49 ℓ
(b)
Remaining water in the tank
= 140 x 70 x 43
= 421400 cm
3 50 ℓ = 50000 mℓ
Total volume of water to drain
= 421400 + 50000
= 471400 mℓ
20 ℓ = 20000 mℓ
Time taken to drain the water
= 471400 ÷ 20000
= 23.57 min
Answer(s): (a) 49 ℓ; (b) 23.57 min