This figure is not drawn to scale. A rectangular glass tank 88 cm by 50 cm by 50 cm has 2 compartments, P and Q, with a water height of 40 cm in P and 18 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 134 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
= 11 x 40 x 50
= 22000 cm
3 Length of Compartment Q
= 88 - 11
= 77 cm
Volume of the water in Compartment Q
= 77 x 50 x 18
= 69300 cm
3 Total volume of water
= 22000 + 69300
= 91300 cm
3 Base area of the glass tank
= 88 x 50
= 4400 cm
2 Height of water
= 91300 ÷ 4400
= 20.75 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment P
= 40 - 20.75
= 19.25 cm
Drop in the volume of Compartment P
= 50 x 11 x 19.25
= 10587.5 cm
3 Volume of water flowed from P to Q in 1 minute
= 10587.5 ÷ 105
≈ 100.8 cm
3 Answer(s): (a) 20.75 cm; (b) 100.8 cm
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