This figure is not drawn to scale. A rectangular glass container 80 cm by 52 cm by 45 cm has 2 compartments, W and X, with a water height of 38 cm in W and 20 cm in X. A hole in the slider caused water to leak from W to X. 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 114 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 W to X in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment W
= 32 x 38 x 52
= 63232 cm
3 Length of Compartment X
= 80 - 32
= 48 cm
Volume of the water in Compartment X
= 48 x 52 x 20
= 49920 cm
3 Total volume of water
= 63232 + 49920
= 113152 cm
3 Base area of the glass container
= 80 x 52
= 4160 cm
2 Height of water
= 113152 ÷ 4160
= 27.2 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment W
= 38 - 27.2
= 10.8 cm
Drop in the volume of Compartment W
= 52 x 32 x 10.8
= 17971.2 cm
3 Volume of water flowed from W to X in 1 minute
= 17971.2 ÷ 75
≈ 239.6 cm
3 Answer(s): (a) 27.2 cm; (b) 239.6 cm
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