This figure is not drawn to scale. A rectangular glass container 70 cm by 58 cm by 41 cm has 2 compartments, X and Y, with a water height of 38 cm in X and 14 cm in Y. A hole in the slider caused water to leak from X to Y. 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 X to Y in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment X
= 14 x 38 x 58
= 30856 cm
3 Length of Compartment Y
= 70 - 14
= 56 cm
Volume of the water in Compartment Y
= 56 x 58 x 14
= 45472 cm
3 Total volume of water
= 30856 + 45472
= 76328 cm
3 Base area of the glass container
= 70 x 58
= 4060 cm
2 Height of water
= 76328 ÷ 4060
= 18.8 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment X
= 38 - 18.8
= 19.2 cm
Drop in the volume of Compartment X
= 58 x 14 x 19.2
= 15590.4 cm
3 Volume of water flowed from X to Y in 1 minute
= 15590.4 ÷ 90
≈ 173.2 cm
3 Answer(s): (a) 18.8 cm; (b) 173.2 cm
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