This figure is not drawn to scale. A rectangular glass container 75 cm by 55 cm by 49 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 115 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
= 29 x 40 x 55
= 63800 cm
3 Length of Compartment X
= 75 - 29
= 46 cm
Volume of the water in Compartment X
= 46 x 55 x 16
= 40480 cm
3 Total volume of water
= 63800 + 40480
= 104280 cm
3 Base area of the glass container
= 75 x 55
= 4125 cm
2 Height of water
= 104280 ÷ 4125
= 25.28 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment W
= 40 - 25.28
= 14.72 cm
Drop in the volume of Compartment W
= 55 x 29 x 14.72
= 23478.4 cm
3 Volume of water flowed from W to X in 1 minute
= 23478.4 ÷ 72
≈ 326.1 cm
3 Answer(s): (a) 25.28 cm; (b) 326.1 cm
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