This figure is not drawn to scale. A rectangular glass tank 84 cm by 52 cm by 43 cm has 2 compartments, S and T, with a water height of 32 cm in S and 17 cm in T. A hole in the slider caused water to leak from S to T. 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 S to T in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment S
= 21 x 32 x 52
= 34944 cm
3 Length of Compartment T
= 84 - 21
= 63 cm
Volume of the water in Compartment T
= 63 x 52 x 17
= 55692 cm
3 Total volume of water
= 34944 + 55692
= 90636 cm
3 Base area of the glass tank
= 84 x 52
= 4368 cm
2 Height of water
= 90636 ÷ 4368
= 20.75 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment S
= 32 - 20.75
= 11.25 cm
Drop in the volume of Compartment S
= 52 x 21 x 11.25
= 12285 cm
3 Volume of water flowed from S to T in 1 minute
= 12285 ÷ 72
≈ 170.6 cm
3 Answer(s): (a) 20.75 cm; (b) 170.6 cm
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