This figure is not drawn to scale. A rectangular glass tank 72 cm by 58 cm by 49 cm has 2 compartments, V and W, with a water height of 40 cm in V and 10 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 tank 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
= 15 x 40 x 58
= 34800 cm
3 Length of Compartment W
= 72 - 15
= 57 cm
Volume of the water in Compartment W
= 57 x 58 x 10
= 33060 cm
3 Total volume of water
= 34800 + 33060
= 67860 cm
3 Base area of the glass tank
= 72 x 58
= 4176 cm
2 Height of water
= 67860 ÷ 4176
= 16.25 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment V
= 40 - 16.25
= 23.75 cm
Drop in the volume of Compartment V
= 58 x 15 x 23.75
= 20662.5 cm
3 Volume of water flowed from V to W in 1 minute
= 20662.5 ÷ 105
≈ 196.8 cm
3 Answer(s): (a) 16.25 cm; (b) 196.8 cm
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