This figure is not drawn to scale. A rectangular glass container 90 cm by 55 cm by 40 cm has 2 compartments, Y and Z, with a water height of 40 cm in Y and 10 cm in Z. A hole in the slider caused water to leak from Y to Z. It was found that the water level in both compartments became the same after some time.
- What is the height of water in the container 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 Y to Z in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment Y
= 36 x 40 x 55
= 79200 cm
3 Length of Compartment Z
= 90 - 36
= 54 cm
Volume of the water in Compartment Z
= 54 x 55 x 10
= 29700 cm
3 Total volume of water
= 79200 + 29700
= 108900 cm
3 Base area of the glass container
= 90 x 55
= 4950 cm
2 Height of water
= 108900 ÷ 4950
= 22 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment Y
= 40 - 22
= 18 cm
Drop in the volume of Compartment Y
= 55 x 36 x 18
= 35640 cm
3 Volume of water flowed from Y to Z in 1 minute
= 35640 ÷ 105
≈ 339.4 cm
3 Answer(s): (a) 22 cm; (b) 339.4 cm
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