This figure is not drawn to scale. A rectangular glass tank 85 cm by 58 cm by 40 cm has 2 compartments, X and Y, with a water height of 37 cm in X and 20 cm in Y. A hole in the slider caused water to leak from X to Y. 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 X to Y in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment X
= 37 x 37 x 58
= 79402 cm
3 Length of Compartment Y
= 85 - 37
= 48 cm
Volume of the water in Compartment Y
= 48 x 58 x 20
= 55680 cm
3 Total volume of water
= 79402 + 55680
= 135082 cm
3 Base area of the glass tank
= 85 x 58
= 4930 cm
2 Height of water
= 135082 ÷ 4930
= 27.4 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment X
= 37 - 27.4
= 9.6 cm
Drop in the volume of Compartment X
= 58 x 37 x 9.6
= 20601.6 cm
3 Volume of water flowed from X to Y in 1 minute
= 20601.6 ÷ 72
≈ 286.1 cm
3 Answer(s): (a) 27.4 cm; (b) 286.1 cm
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