This figure is not drawn to scale. A rectangular glass container 85 cm by 60 cm by 46 cm has 2 compartments, D and E, with a water height of 35 cm in D and 18 cm in E. A hole in the slider caused water to leak from D to E. 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 D to E in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment D
= 12 x 35 x 60
= 25200 cm
3 Length of Compartment E
= 85 - 12
= 73 cm
Volume of the water in Compartment E
= 73 x 60 x 18
= 78840 cm
3 Total volume of water
= 25200 + 78840
= 104040 cm
3 Base area of the glass container
= 85 x 60
= 5100 cm
2 Height of water
= 104040 ÷ 5100
= 20.4 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment D
= 35 - 20.4
= 14.6 cm
Drop in the volume of Compartment D
= 60 x 12 x 14.6
= 10512 cm
3 Volume of water flowed from D to E in 1 minute
= 10512 ÷ 72
≈ 146.0 cm
3 Answer(s): (a) 20.4 cm; (b) 146.0 cm
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