This figure is not drawn to scale. A rectangular glass tank 80 cm by 54 cm by 46 cm has 2 compartments, W and X, with a water height of 34 cm in W and 10 cm in X. A hole in the slider caused water to leak from W to X. 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 134 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 W to X in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment W
= 23 x 34 x 54
= 42228 cm
3 Length of Compartment X
= 80 - 23
= 57 cm
Volume of the water in Compartment X
= 57 x 54 x 10
= 30780 cm
3 Total volume of water
= 42228 + 30780
= 73008 cm
3 Base area of the glass tank
= 80 x 54
= 4320 cm
2 Height of water
= 73008 ÷ 4320
= 16.9 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment W
= 34 - 16.9
= 17.1 cm
Drop in the volume of Compartment W
= 54 x 23 x 17.1
= 21238.2 cm
3 Volume of water flowed from W to X in 1 minute
= 21238.2 ÷ 105
≈ 202.3 cm
3 Answer(s): (a) 16.9 cm; (b) 202.3 cm
3