This figure is not drawn to scale. A rectangular glass container 76 cm by 50 cm by 42 cm has 2 compartments, H and J, with a water height of 31 cm in H and 12 cm in J. A hole in the slider caused water to leak from H to J. 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 H to J in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment H
= 13 x 31 x 50
= 20150 cm
3 Length of Compartment J
= 76 - 13
= 63 cm
Volume of the water in Compartment J
= 63 x 50 x 12
= 37800 cm
3 Total volume of water
= 20150 + 37800
= 57950 cm
3 Base area of the glass container
= 76 x 50
= 3800 cm
2 Height of water
= 57950 ÷ 3800
= 15.25 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment H
= 31 - 15.25
= 15.75 cm
Drop in the volume of Compartment H
= 50 x 13 x 15.75
= 10237.5 cm
3 Volume of water flowed from H to J in 1 minute
= 10237.5 ÷ 105
≈ 97.5 cm
3 Answer(s): (a) 15.25 cm; (b) 97.5 cm
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