This figure is not drawn to scale. A rectangular glass tank 75 cm by 60 cm by 41 cm has 2 compartments, P and Q, with a water height of 30 cm in P and 11 cm in Q. A hole in the slider caused water to leak from P to Q. 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 112 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 P to Q in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment P
= 39 x 30 x 60
= 70200 cm
3 Length of Compartment Q
= 75 - 39
= 36 cm
Volume of the water in Compartment Q
= 36 x 60 x 11
= 23760 cm
3 Total volume of water
= 70200 + 23760
= 93960 cm
3 Base area of the glass tank
= 75 x 60
= 4500 cm
2 Height of water
= 93960 ÷ 4500
= 20.88 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment P
= 30 - 20.88
= 9.12 cm
Drop in the volume of Compartment P
= 60 x 39 x 9.12
= 21340.8 cm
3 Volume of water flowed from P to Q in 1 minute
= 21340.8 ÷ 90
≈ 237.1 cm
3 Answer(s): (a) 20.88 cm; (b) 237.1 cm
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