This figure is not drawn to scale. A rectangular glass tank 75 cm by 60 cm by 42 cm has 2 compartments, R and S, with a water height of 30 cm in R and 11 cm in S. A hole in the slider caused water to leak from R to S. 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 112 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 R to S in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment R
= 27 x 30 x 60
= 48600 cm
3 Length of Compartment S
= 75 - 27
= 48 cm
Volume of the water in Compartment S
= 48 x 60 x 11
= 31680 cm
3 Total volume of water
= 48600 + 31680
= 80280 cm
3 Base area of the glass tank
= 75 x 60
= 4500 cm
2 Height of water
= 80280 ÷ 4500
= 17.84 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment R
= 30 - 17.84
= 12.16 cm
Drop in the volume of Compartment R
= 60 x 27 x 12.16
= 19699.2 cm
3 Volume of water flowed from R to S in 1 minute
= 19699.2 ÷ 90
≈ 218.9 cm
3 Answer(s): (a) 17.84 cm; (b) 218.9 cm
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