This figure is not drawn to scale. A rectangular glass tank 75 cm by 56 cm by 41 cm has 2 compartments, G and H, with a water height of 39 cm in G and 10 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 134 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
= 15 x 39 x 56
= 32760 cm
3 Length of Compartment H
= 75 - 15
= 60 cm
Volume of the water in Compartment H
= 60 x 56 x 10
= 33600 cm
3 Total volume of water
= 32760 + 33600
= 66360 cm
3 Base area of the glass tank
= 75 x 56
= 4200 cm
2 Height of water
= 66360 ÷ 4200
= 15.8 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment G
= 39 - 15.8
= 23.2 cm
Drop in the volume of Compartment G
= 56 x 15 x 23.2
= 19488 cm
3 Volume of water flowed from G to H in 1 minute
= 19488 ÷ 105
≈ 185.6 cm
3 Answer(s): (a) 15.8 cm; (b) 185.6 cm
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