This figure is not drawn to scale. A rectangular glass tank 72 cm by 55 cm by 46 cm has 2 compartments, G and H, with a water height of 35 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
= 33 x 35 x 55
= 63525 cm
3 Length of Compartment H
= 72 - 33
= 39 cm
Volume of the water in Compartment H
= 39 x 55 x 11
= 23595 cm
3 Total volume of water
= 63525 + 23595
= 87120 cm
3 Base area of the glass tank
= 72 x 55
= 3960 cm
2 Height of water
= 87120 ÷ 3960
= 22 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment G
= 35 - 22
= 13 cm
Drop in the volume of Compartment G
= 55 x 33 x 13
= 23595 cm
3 Volume of water flowed from G to H in 1 minute
= 23595 ÷ 72
≈ 327.7 cm
3 Answer(s): (a) 22 cm; (b) 327.7 cm
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