This figure is not drawn to scale. A rectangular glass tank 80 cm by 53 cm by 40 cm has 2 compartments, G and H, with a water height of 34 cm in G and 11 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
= 28 x 34 x 53
= 50456 cm
3 Length of Compartment H
= 80 - 28
= 52 cm
Volume of the water in Compartment H
= 52 x 53 x 11
= 30316 cm
3 Total volume of water
= 50456 + 30316
= 80772 cm
3 Base area of the glass tank
= 80 x 53
= 4240 cm
2 Height of water
= 80772 ÷ 4240
= 19.05 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment G
= 34 - 19.05
= 14.95 cm
Drop in the volume of Compartment G
= 53 x 28 x 14.95
= 22185.8 cm
3 Volume of water flowed from G to H in 1 minute
= 22185.8 ÷ 72
≈ 308.1 cm
3 Answer(s): (a) 19.05 cm; (b) 308.1 cm
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