This figure is not drawn to scale. A rectangular glass container 80 cm by 56 cm by 48 cm has 2 compartments, Y and Z, with a water height of 39 cm in Y and 12 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 39 x 56
= 78624 cm
3 Length of Compartment Z
= 80 - 36
= 44 cm
Volume of the water in Compartment Z
= 44 x 56 x 12
= 29568 cm
3 Total volume of water
= 78624 + 29568
= 108192 cm
3 Base area of the glass container
= 80 x 56
= 4480 cm
2 Height of water
= 108192 ÷ 4480
= 24.15 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment Y
= 39 - 24.15
= 14.85 cm
Drop in the volume of Compartment Y
= 56 x 36 x 14.85
= 29937.6 cm
3 Volume of water flowed from Y to Z in 1 minute
= 29937.6 ÷ 105
≈ 285.1 cm
3 Answer(s): (a) 24.15 cm; (b) 285.1 cm
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