This figure is not drawn to scale. A rectangular glass tank 80 cm by 50 cm by 47 cm has 2 compartments, H and J, with a water height of 39 cm in H and 12 cm in J. A hole in the slider caused water to leak from H to J. 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 H to J in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment H
= 28 x 39 x 50
= 54600 cm
3 Length of Compartment J
= 80 - 28
= 52 cm
Volume of the water in Compartment J
= 52 x 50 x 12
= 31200 cm
3 Total volume of water
= 54600 + 31200
= 85800 cm
3 Base area of the glass tank
= 80 x 50
= 4000 cm
2 Height of water
= 85800 ÷ 4000
= 21.45 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment H
= 39 - 21.45
= 17.55 cm
Drop in the volume of Compartment H
= 50 x 28 x 17.55
= 24570 cm
3 Volume of water flowed from H to J in 1 minute
= 24570 ÷ 72
≈ 341.3 cm
3 Answer(s): (a) 21.45 cm; (b) 341.3 cm
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