This figure is not drawn to scale. A rectangular glass tank 85 cm by 59 cm by 44 cm has 2 compartments, P and Q, with a water height of 31 cm in P and 14 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
= 16 x 31 x 59
= 29264 cm
3 Length of Compartment Q
= 85 - 16
= 69 cm
Volume of the water in Compartment Q
= 69 x 59 x 14
= 56994 cm
3 Total volume of water
= 29264 + 56994
= 86258 cm
3 Base area of the glass tank
= 85 x 59
= 5015 cm
2 Height of water
= 86258 ÷ 5015
= 17.2 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment P
= 31 - 17.2
= 13.8 cm
Drop in the volume of Compartment P
= 59 x 16 x 13.8
= 13027.2 cm
3 Volume of water flowed from P to Q in 1 minute
= 13027.2 ÷ 105
≈ 124.1 cm
3 Answer(s): (a) 17.2 cm; (b) 124.1 cm
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