This figure is not drawn to scale. A rectangular glass tank 75 cm by 51 cm by 50 cm has 2 compartments, W and X, with a water height of 35 cm in W and 11 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
= 17 x 35 x 51
= 30345 cm
3 Length of Compartment X
= 75 - 17
= 58 cm
Volume of the water in Compartment X
= 58 x 51 x 11
= 32538 cm
3 Total volume of water
= 30345 + 32538
= 62883 cm
3 Base area of the glass tank
= 75 x 51
= 3825 cm
2 Height of water
= 62883 ÷ 3825
= 16.44 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment W
= 35 - 16.44
= 18.56 cm
Drop in the volume of Compartment W
= 51 x 17 x 18.56
= 16091.52 cm
3 Volume of water flowed from W to X in 1 minute
= 16091.52 ÷ 105
≈ 153.3 cm
3 Answer(s): (a) 16.44 cm; (b) 153.3 cm
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