This figure is not drawn to scale. A rectangular glass container 75 cm by 59 cm by 50 cm has 2 compartments, V and W, with a water height of 40 cm in V and 19 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 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 V to W in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment V
= 39 x 40 x 59
= 92040 cm
3 Length of Compartment W
= 75 - 39
= 36 cm
Volume of the water in Compartment W
= 36 x 59 x 19
= 40356 cm
3 Total volume of water
= 92040 + 40356
= 132396 cm
3 Base area of the glass container
= 75 x 59
= 4425 cm
2 Height of water
= 132396 ÷ 4425
= 29.92 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment V
= 40 - 29.92
= 10.08 cm
Drop in the volume of Compartment V
= 59 x 39 x 10.08
= 23194.08 cm
3 Volume of water flowed from V to W in 1 minute
= 23194.08 ÷ 105
≈ 220.9 cm
3 Answer(s): (a) 29.92 cm; (b) 220.9 cm
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