This figure is not drawn to scale. A rectangular glass container 80 cm by 57 cm by 45 cm has 2 compartments, W and X, with a water height of 40 cm in W and 16 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 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 W to X in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment W
= 33 x 40 x 57
= 75240 cm
3 Length of Compartment X
= 80 - 33
= 47 cm
Volume of the water in Compartment X
= 47 x 57 x 16
= 42864 cm
3 Total volume of water
= 75240 + 42864
= 118104 cm
3 Base area of the glass container
= 80 x 57
= 4560 cm
2 Height of water
= 118104 ÷ 4560
= 25.9 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment W
= 40 - 25.9
= 14.1 cm
Drop in the volume of Compartment W
= 57 x 33 x 14.1
= 26522.1 cm
3 Volume of water flowed from W to X in 1 minute
= 26522.1 ÷ 105
≈ 252.6 cm
3 Answer(s): (a) 25.9 cm; (b) 252.6 cm
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