This figure is not drawn to scale. A rectangular glass container 85 cm by 56 cm by 42 cm has 2 compartments, Y and Z, with a water height of 33 cm in Y and 16 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 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 Y to Z in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment Y
= 32 x 33 x 56
= 59136 cm
3 Length of Compartment Z
= 85 - 32
= 53 cm
Volume of the water in Compartment Z
= 53 x 56 x 16
= 47488 cm
3 Total volume of water
= 59136 + 47488
= 106624 cm
3 Base area of the glass container
= 85 x 56
= 4760 cm
2 Height of water
= 106624 ÷ 4760
= 22.4 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment Y
= 33 - 22.4
= 10.6 cm
Drop in the volume of Compartment Y
= 56 x 32 x 10.6
= 18995.2 cm
3 Volume of water flowed from Y to Z in 1 minute
= 18995.2 ÷ 90
≈ 211.1 cm
3 Answer(s): (a) 22.4 cm; (b) 211.1 cm
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