This figure is not drawn to scale. A rectangular glass tank 80 cm by 52 cm by 50 cm has 2 compartments, N and P, with a water height of 37 cm in N and 15 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 134 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
= 10 x 37 x 52
= 19240 cm
3 Length of Compartment P
= 80 - 10
= 70 cm
Volume of the water in Compartment P
= 70 x 52 x 15
= 54600 cm
3 Total volume of water
= 19240 + 54600
= 73840 cm
3 Base area of the glass tank
= 80 x 52
= 4160 cm
2 Height of water
= 73840 ÷ 4160
= 17.75 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment N
= 37 - 17.75
= 19.25 cm
Drop in the volume of Compartment N
= 52 x 10 x 19.25
= 10010 cm
3 Volume of water flowed from N to P in 1 minute
= 10010 ÷ 105
≈ 95.3 cm
3 Answer(s): (a) 17.75 cm; (b) 95.3 cm
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