This figure is not drawn to scale. A rectangular glass tank 75 cm by 55 cm by 44 cm has 2 compartments, N and P, with a water height of 32 cm in N and 10 cm in P. A hole in the slider caused water to leak from N to P. 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 N to P in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment N
= 36 x 32 x 55
= 63360 cm
3 Length of Compartment P
= 75 - 36
= 39 cm
Volume of the water in Compartment P
= 39 x 55 x 10
= 21450 cm
3 Total volume of water
= 63360 + 21450
= 84810 cm
3 Base area of the glass tank
= 75 x 55
= 4125 cm
2 Height of water
= 84810 ÷ 4125
= 20.56 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment N
= 32 - 20.56
= 11.44 cm
Drop in the volume of Compartment N
= 55 x 36 x 11.44
= 22651.2 cm
3 Volume of water flowed from N to P in 1 minute
= 22651.2 ÷ 72
≈ 314.6 cm
3 Answer(s): (a) 20.56 cm; (b) 314.6 cm
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