This figure is not drawn to scale. A rectangular glass tank 90 cm by 52 cm by 40 cm has 2 compartments, T and U, with a water height of 37 cm in T and 18 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
= 18 x 37 x 52
= 34632 cm
3 Length of Compartment U
= 90 - 18
= 72 cm
Volume of the water in Compartment U
= 72 x 52 x 18
= 67392 cm
3 Total volume of water
= 34632 + 67392
= 102024 cm
3 Base area of the glass tank
= 90 x 52
= 4680 cm
2 Height of water
= 102024 ÷ 4680
= 21.8 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment T
= 37 - 21.8
= 15.2 cm
Drop in the volume of Compartment T
= 52 x 18 x 15.2
= 14227.2 cm
3 Volume of water flowed from T to U in 1 minute
= 14227.2 ÷ 72
≈ 197.6 cm
3 Answer(s): (a) 21.8 cm; (b) 197.6 cm
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