This figure is not drawn to scale. A rectangular glass container 80 cm by 50 cm by 45 cm has 2 compartments, V and W, with a water height of 40 cm in V and 20 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 115 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
= 30 x 40 x 50
= 60000 cm
3 Length of Compartment W
= 80 - 30
= 50 cm
Volume of the water in Compartment W
= 50 x 50 x 20
= 50000 cm
3 Total volume of water
= 60000 + 50000
= 110000 cm
3 Base area of the glass container
= 80 x 50
= 4000 cm
2 Height of water
= 110000 ÷ 4000
= 27.5 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment V
= 40 - 27.5
= 12.5 cm
Drop in the volume of Compartment V
= 50 x 30 x 12.5
= 18750 cm
3 Volume of water flowed from V to W in 1 minute
= 18750 ÷ 72
≈ 260.4 cm
3 Answer(s): (a) 27.5 cm; (b) 260.4 cm
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