This figure is not drawn to scale. A rectangular glass tank 90 cm by 60 cm by 41 cm has 2 compartments, Q and R, with a water height of 37 cm in Q and 14 cm in R. A hole in the slider caused water to leak from Q to R. 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 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 Q to R in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment Q
= 18 x 37 x 60
= 39960 cm
3 Length of Compartment R
= 90 - 18
= 72 cm
Volume of the water in Compartment R
= 72 x 60 x 14
= 60480 cm
3 Total volume of water
= 39960 + 60480
= 100440 cm
3 Base area of the glass tank
= 90 x 60
= 5400 cm
2 Height of water
= 100440 ÷ 5400
= 18.6 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment Q
= 37 - 18.6
= 18.4 cm
Drop in the volume of Compartment Q
= 60 x 18 x 18.4
= 19872 cm
3 Volume of water flowed from Q to R in 1 minute
= 19872 ÷ 75
≈ 265 cm
3 Answer(s): (a) 18.6 cm; (b) 265 cm
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