This figure is not drawn to scale. A rectangular glass container 78 cm by 60 cm by 47 cm has 2 compartments, V and W, with a water height of 31 cm in V and 18 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
= 30 x 31 x 60
= 55800 cm
3 Length of Compartment W
= 78 - 30
= 48 cm
Volume of the water in Compartment W
= 48 x 60 x 18
= 51840 cm
3 Total volume of water
= 55800 + 51840
= 107640 cm
3 Base area of the glass container
= 78 x 60
= 4680 cm
2 Height of water
= 107640 ÷ 4680
= 23 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment V
= 31 - 23
= 8 cm
Drop in the volume of Compartment V
= 60 x 30 x 8
= 14400 cm
3 Volume of water flowed from V to W in 1 minute
= 14400 ÷ 105
≈ 137.1 cm
3 Answer(s): (a) 23 cm; (b) 137.1 cm
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