This figure is not drawn to scale. A rectangular glass tank 75 cm by 56 cm by 47 cm has 2 compartments, W and X, with a water height of 32 cm in W and 11 cm in X. A hole in the slider caused water to leak from W to X. 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 114 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 W to X in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment W
= 30 x 32 x 56
= 53760 cm
3 Length of Compartment X
= 75 - 30
= 45 cm
Volume of the water in Compartment X
= 45 x 56 x 11
= 27720 cm
3 Total volume of water
= 53760 + 27720
= 81480 cm
3 Base area of the glass tank
= 75 x 56
= 4200 cm
2 Height of water
= 81480 ÷ 4200
= 19.4 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment W
= 32 - 19.4
= 12.6 cm
Drop in the volume of Compartment W
= 56 x 30 x 12.6
= 21168 cm
3 Volume of water flowed from W to X in 1 minute
= 21168 ÷ 75
≈ 282.2 cm
3 Answer(s): (a) 19.4 cm; (b) 282.2 cm
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