This figure is not drawn to scale. A rectangular glass tank 75 cm by 52 cm by 49 cm has 2 compartments, G and H, with a water height of 34 cm in G and 16 cm in H. A hole in the slider caused water to leak from G to H. 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 G to H in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment G
= 30 x 34 x 52
= 53040 cm
3 Length of Compartment H
= 75 - 30
= 45 cm
Volume of the water in Compartment H
= 45 x 52 x 16
= 37440 cm
3 Total volume of water
= 53040 + 37440
= 90480 cm
3 Base area of the glass tank
= 75 x 52
= 3900 cm
2 Height of water
= 90480 ÷ 3900
= 23.2 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment G
= 34 - 23.2
= 10.8 cm
Drop in the volume of Compartment G
= 52 x 30 x 10.8
= 16848 cm
3 Volume of water flowed from G to H in 1 minute
= 16848 ÷ 72
≈ 234.0 cm
3 Answer(s): (a) 23.2 cm; (b) 234.0 cm
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