This figure is not drawn to scale. A rectangular glass container 88 cm by 50 cm by 44 cm has 2 compartments, V and W, with a water height of 34 cm in V and 12 cm in W. A hole in the slider caused water to leak from V to W. 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 114 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 V to W in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment V
= 17 x 34 x 50
= 28900 cm
3 Length of Compartment W
= 88 - 17
= 71 cm
Volume of the water in Compartment W
= 71 x 50 x 12
= 42600 cm
3 Total volume of water
= 28900 + 42600
= 71500 cm
3 Base area of the glass container
= 88 x 50
= 4400 cm
2 Height of water
= 71500 ÷ 4400
= 16.25 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment V
= 34 - 16.25
= 17.75 cm
Drop in the volume of Compartment V
= 50 x 17 x 17.75
= 15087.5 cm
3 Volume of water flowed from V to W in 1 minute
= 15087.5 ÷ 75
≈ 201.2 cm
3 Answer(s): (a) 16.25 cm; (b) 201.2 cm
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