This figure is not drawn to scale. A rectangular glass tank 75 cm by 60 cm by 40 cm has 2 compartments, S and T, with a water height of 39 cm in S and 14 cm in T. A hole in the slider caused water to leak from S to T. It was found that the water level in both compartments became the same after some time.
- What is the height of water in the tank now?
- It took 114 h for the water in both compartments to reach the same level. Assuming that water leaked at a constant rate, how much water flowed from S to T in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment S
= 18 x 39 x 60
= 42120 cm
3 Length of Compartment T
= 75 - 18
= 57 cm
Volume of the water in Compartment T
= 57 x 60 x 14
= 47880 cm
3 Total volume of water
= 42120 + 47880
= 90000 cm
3 Base area of the glass tank
= 75 x 60
= 4500 cm
2 Height of water
= 90000 ÷ 4500
= 20 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment S
= 39 - 20
= 19 cm
Drop in the volume of Compartment S
= 60 x 18 x 19
= 20520 cm
3 Volume of water flowed from S to T in 1 minute
= 20520 ÷ 75
≈ 273.6 cm
3 Answer(s): (a) 20 cm; (b) 273.6 cm
3