This figure is not drawn to scale. A rectangular glass tank 70 cm by 52 cm by 50 cm has 2 compartments, V and W, with a water height of 30 cm in V and 16 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
= 37 x 30 x 52
= 57720 cm
3 Length of Compartment W
= 70 - 37
= 33 cm
Volume of the water in Compartment W
= 33 x 52 x 16
= 27456 cm
3 Total volume of water
= 57720 + 27456
= 85176 cm
3 Base area of the glass tank
= 70 x 52
= 3640 cm
2 Height of water
= 85176 ÷ 3640
= 23.4 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment V
= 30 - 23.4
= 6.6 cm
Drop in the volume of Compartment V
= 52 x 37 x 6.6
= 12698.4 cm
3 Volume of water flowed from V to W in 1 minute
= 12698.4 ÷ 105
≈ 120.9 cm
3 Answer(s): (a) 23.4 cm; (b) 120.9 cm
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