This figure is not drawn to scale. A rectangular glass container 75 cm by 53 cm by 48 cm has 2 compartments, D and E, with a water height of 34 cm in D and 14 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 114 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
= 15 x 34 x 53
= 27030 cm
3 Length of Compartment E
= 75 - 15
= 60 cm
Volume of the water in Compartment E
= 60 x 53 x 14
= 44520 cm
3 Total volume of water
= 27030 + 44520
= 71550 cm
3 Base area of the glass container
= 75 x 53
= 3975 cm
2 Height of water
= 71550 ÷ 3975
= 18 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment D
= 34 - 18
= 16 cm
Drop in the volume of Compartment D
= 53 x 15 x 16
= 12720 cm
3 Volume of water flowed from D to E in 1 minute
= 12720 ÷ 75
≈ 169.6 cm
3 Answer(s): (a) 18 cm; (b) 169.6 cm
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