This figure is not drawn to scale. A rectangular glass tank 75 cm by 58 cm by 44 cm has 2 compartments, D and E, with a water height of 37 cm in D and 20 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
= 21 x 37 x 58
= 45066 cm
3 Length of Compartment E
= 75 - 21
= 54 cm
Volume of the water in Compartment E
= 54 x 58 x 20
= 62640 cm
3 Total volume of water
= 45066 + 62640
= 107706 cm
3 Base area of the glass tank
= 75 x 58
= 4350 cm
2 Height of water
= 107706 ÷ 4350
= 24.76 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment D
= 37 - 24.76
= 12.24 cm
Drop in the volume of Compartment D
= 58 x 21 x 12.24
= 14908.32 cm
3 Volume of water flowed from D to E in 1 minute
= 14908.32 ÷ 72
≈ 207.1 cm
3 Answer(s): (a) 24.76 cm; (b) 207.1 cm
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