This figure is not drawn to scale. A rectangular glass container 88 cm by 57 cm by 45 cm has 2 compartments, F and G, with a water height of 39 cm in F and 17 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 112 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
= 21 x 39 x 57
= 46683 cm
3 Length of Compartment G
= 88 - 21
= 67 cm
Volume of the water in Compartment G
= 67 x 57 x 17
= 64923 cm
3 Total volume of water
= 46683 + 64923
= 111606 cm
3 Base area of the glass container
= 88 x 57
= 5016 cm
2 Height of water
= 111606 ÷ 5016
= 22.25 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment F
= 39 - 22.25
= 16.75 cm
Drop in the volume of Compartment F
= 57 x 21 x 16.75
= 20049.75 cm
3 Volume of water flowed from F to G in 1 minute
= 20049.75 ÷ 90
≈ 222.8 cm
3 Answer(s): (a) 22.25 cm; (b) 222.8 cm
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