This figure is not drawn to scale. A rectangular glass tank 80 cm by 59 cm by 43 cm has 2 compartments, F and G, with a water height of 30 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 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 F to G in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment F
= 18 x 30 x 59
= 31860 cm
3 Length of Compartment G
= 80 - 18
= 62 cm
Volume of the water in Compartment G
= 62 x 59 x 20
= 73160 cm
3 Total volume of water
= 31860 + 73160
= 105020 cm
3 Base area of the glass tank
= 80 x 59
= 4720 cm
2 Height of water
= 105020 ÷ 4720
= 22.25 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment F
= 30 - 22.25
= 7.75 cm
Drop in the volume of Compartment F
= 59 x 18 x 7.75
= 8230.5 cm
3 Volume of water flowed from F to G in 1 minute
= 8230.5 ÷ 105
≈ 78.4 cm
3 Answer(s): (a) 22.25 cm; (b) 78.4 cm
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