This figure is not drawn to scale. A rectangular glass container 75 cm by 54 cm by 43 cm has 2 compartments, H and J, with a water height of 31 cm in H and 11 cm in J. A hole in the slider caused water to leak from H to J. 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 H to J in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment H
= 27 x 31 x 54
= 45198 cm
3 Length of Compartment J
= 75 - 27
= 48 cm
Volume of the water in Compartment J
= 48 x 54 x 11
= 28512 cm
3 Total volume of water
= 45198 + 28512
= 73710 cm
3 Base area of the glass container
= 75 x 54
= 4050 cm
2 Height of water
= 73710 ÷ 4050
= 18.2 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment H
= 31 - 18.2
= 12.8 cm
Drop in the volume of Compartment H
= 54 x 27 x 12.8
= 18662.4 cm
3 Volume of water flowed from H to J in 1 minute
= 18662.4 ÷ 72
≈ 259.2 cm
3 Answer(s): (a) 18.2 cm; (b) 259.2 cm
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