This figure is not drawn to scale. A rectangular glass tank 75 cm by 50 cm by 42 cm has 2 compartments, U and V, with a water height of 33 cm in U and 12 cm in V. A hole in the slider caused water to leak from U to V. 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 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 U to V in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment U
= 29 x 33 x 50
= 47850 cm
3 Length of Compartment V
= 75 - 29
= 46 cm
Volume of the water in Compartment V
= 46 x 50 x 12
= 27600 cm
3 Total volume of water
= 47850 + 27600
= 75450 cm
3 Base area of the glass tank
= 75 x 50
= 3750 cm
2 Height of water
= 75450 ÷ 3750
= 20.12 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment U
= 33 - 20.12
= 12.88 cm
Drop in the volume of Compartment U
= 50 x 29 x 12.88
= 18676 cm
3 Volume of water flowed from U to V in 1 minute
= 18676 ÷ 72
≈ 259.4 cm
3 Answer(s): (a) 20.12 cm; (b) 259.4 cm
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