This figure is not drawn to scale. A rectangular glass container 75 cm by 50 cm by 49 cm has 2 compartments, F and G, with a water height of 35 cm in F and 18 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 container 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
= 15 x 35 x 50
= 26250 cm
3 Length of Compartment G
= 75 - 15
= 60 cm
Volume of the water in Compartment G
= 60 x 50 x 18
= 54000 cm
3 Total volume of water
= 26250 + 54000
= 80250 cm
3 Base area of the glass container
= 75 x 50
= 3750 cm
2 Height of water
= 80250 ÷ 3750
= 21.4 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment F
= 35 - 21.4
= 13.6 cm
Drop in the volume of Compartment F
= 50 x 15 x 13.6
= 10200 cm
3 Volume of water flowed from F to G in 1 minute
= 10200 ÷ 105
≈ 97.1 cm
3 Answer(s): (a) 21.4 cm; (b) 97.1 cm
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