This figure is not drawn to scale. A rectangular glass container 74 cm by 60 cm by 42 cm has 2 compartments, E and F, with a water height of 40 cm in E and 10 cm in F. A hole in the slider caused water to leak from E to F. 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 E to F in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment E
= 37 x 40 x 60
= 88800 cm
3 Length of Compartment F
= 74 - 37
= 37 cm
Volume of the water in Compartment F
= 37 x 60 x 10
= 22200 cm
3 Total volume of water
= 88800 + 22200
= 111000 cm
3 Base area of the glass container
= 74 x 60
= 4440 cm
2 Height of water
= 111000 ÷ 4440
= 25 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment E
= 40 - 25
= 15 cm
Drop in the volume of Compartment E
= 60 x 37 x 15
= 33300 cm
3 Volume of water flowed from E to F in 1 minute
= 33300 ÷ 72
≈ 462.5 cm
3 Answer(s): (a) 25 cm; (b) 462.5 cm
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