This figure is not drawn to scale. A rectangular glass tank 80 cm by 54 cm by 47 cm has 2 compartments, T and U, with a water height of 35 cm in T and 13 cm in U. A hole in the slider caused water to leak from T to U. 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 T to U in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment T
= 12 x 35 x 54
= 22680 cm
3 Length of Compartment U
= 80 - 12
= 68 cm
Volume of the water in Compartment U
= 68 x 54 x 13
= 47736 cm
3 Total volume of water
= 22680 + 47736
= 70416 cm
3 Base area of the glass tank
= 80 x 54
= 4320 cm
2 Height of water
= 70416 ÷ 4320
= 16.3 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment T
= 35 - 16.3
= 18.7 cm
Drop in the volume of Compartment T
= 54 x 12 x 18.7
= 12117.6 cm
3 Volume of water flowed from T to U in 1 minute
= 12117.6 ÷ 72
≈ 168.3 cm
3 Answer(s): (a) 16.3 cm; (b) 168.3 cm
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