This figure is not drawn to scale. A rectangular glass tank 70 cm by 55 cm by 43 cm has 2 compartments, G and H, with a water height of 37 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 114 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
= 33 x 37 x 55
= 67155 cm
3 Length of Compartment H
= 70 - 33
= 37 cm
Volume of the water in Compartment H
= 37 x 55 x 16
= 32560 cm
3 Total volume of water
= 67155 + 32560
= 99715 cm
3 Base area of the glass tank
= 70 x 55
= 3850 cm
2 Height of water
= 99715 ÷ 3850
= 25.9 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment G
= 37 - 25.9
= 11.1 cm
Drop in the volume of Compartment G
= 55 x 33 x 11.1
= 20146.5 cm
3 Volume of water flowed from G to H in 1 minute
= 20146.5 ÷ 75
≈ 268.6 cm
3 Answer(s): (a) 25.9 cm; (b) 268.6 cm
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