This figure is not drawn to scale. A rectangular glass tank 75 cm by 50 cm by 42 cm has 2 compartments, J and K, with a water height of 30 cm in J and 19 cm in K. A hole in the slider caused water to leak from J to K. 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 J to K in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment J
= 36 x 30 x 50
= 54000 cm
3 Length of Compartment K
= 75 - 36
= 39 cm
Volume of the water in Compartment K
= 39 x 50 x 19
= 37050 cm
3 Total volume of water
= 54000 + 37050
= 91050 cm
3 Base area of the glass tank
= 75 x 50
= 3750 cm
2 Height of water
= 91050 ÷ 3750
= 24.28 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment J
= 30 - 24.28
= 5.72 cm
Drop in the volume of Compartment J
= 50 x 36 x 5.72
= 10296 cm
3 Volume of water flowed from J to K in 1 minute
= 10296 ÷ 72
≈ 143.0 cm
3 Answer(s): (a) 24.28 cm; (b) 143.0 cm
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