This figure is not drawn to scale. A rectangular glass tank 84 cm by 56 cm by 49 cm has 2 compartments, W and X, with a water height of 34 cm in W and 20 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 115 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
= 21 x 34 x 56
= 39984 cm
3 Length of Compartment X
= 84 - 21
= 63 cm
Volume of the water in Compartment X
= 63 x 56 x 20
= 70560 cm
3 Total volume of water
= 39984 + 70560
= 110544 cm
3 Base area of the glass tank
= 84 x 56
= 4704 cm
2 Height of water
= 110544 ÷ 4704
= 23.5 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment W
= 34 - 23.5
= 10.5 cm
Drop in the volume of Compartment W
= 56 x 21 x 10.5
= 12348 cm
3 Volume of water flowed from W to X in 1 minute
= 12348 ÷ 72
≈ 171.5 cm
3 Answer(s): (a) 23.5 cm; (b) 171.5 cm
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