This figure is not drawn to scale. A rectangular glass tank 77 cm by 50 cm by 42 cm has 2 compartments, F and G, with a water height of 34 cm in F and 20 cm in G. A hole in the slider caused water to leak from F to G. 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 F to G in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment F
= 33 x 34 x 50
= 56100 cm
3 Length of Compartment G
= 77 - 33
= 44 cm
Volume of the water in Compartment G
= 44 x 50 x 20
= 44000 cm
3 Total volume of water
= 56100 + 44000
= 100100 cm
3 Base area of the glass tank
= 77 x 50
= 3850 cm
2 Height of water
= 100100 ÷ 3850
= 26 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment F
= 34 - 26
= 8 cm
Drop in the volume of Compartment F
= 50 x 33 x 8
= 13200 cm
3 Volume of water flowed from F to G in 1 minute
= 13200 ÷ 72
≈ 183.3 cm
3 Answer(s): (a) 26 cm; (b) 183.3 cm
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