This figure is not drawn to scale. A rectangular glass tank 80 cm by 50 cm by 46 cm has 2 compartments, E and F, with a water height of 37 cm in E and 15 cm in F. A hole in the slider caused water to leak from E to F. 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 E to F in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment E
= 14 x 37 x 50
= 25900 cm
3 Length of Compartment F
= 80 - 14
= 66 cm
Volume of the water in Compartment F
= 66 x 50 x 15
= 49500 cm
3 Total volume of water
= 25900 + 49500
= 75400 cm
3 Base area of the glass tank
= 80 x 50
= 4000 cm
2 Height of water
= 75400 ÷ 4000
= 18.85 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment E
= 37 - 18.85
= 18.15 cm
Drop in the volume of Compartment E
= 50 x 14 x 18.15
= 12705 cm
3 Volume of water flowed from E to F in 1 minute
= 12705 ÷ 90
≈ 141.2 cm
3 Answer(s): (a) 18.85 cm; (b) 141.2 cm
3