This figure is not drawn to scale. A rectangular glass tank 81 cm by 58 cm by 41 cm has 2 compartments, D and E, with a water height of 39 cm in D and 12 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 tank 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
= 30 x 39 x 58
= 67860 cm
3 Length of Compartment E
= 81 - 30
= 51 cm
Volume of the water in Compartment E
= 51 x 58 x 12
= 35496 cm
3 Total volume of water
= 67860 + 35496
= 103356 cm
3 Base area of the glass tank
= 81 x 58
= 4698 cm
2 Height of water
= 103356 ÷ 4698
= 22 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment D
= 39 - 22
= 17 cm
Drop in the volume of Compartment D
= 58 x 30 x 17
= 29580 cm
3 Volume of water flowed from D to E in 1 minute
= 29580 ÷ 72
≈ 410.8 cm
3 Answer(s): (a) 22 cm; (b) 410.8 cm
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