This figure is not drawn to scale. A rectangular glass tank 72 cm by 57 cm by 49 cm has 2 compartments, F and G, with a water height of 34 cm in F and 16 cm in G. A hole in the slider caused water to leak from F to G. 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 F to G in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment F
= 15 x 34 x 57
= 29070 cm
3 Length of Compartment G
= 72 - 15
= 57 cm
Volume of the water in Compartment G
= 57 x 57 x 16
= 51984 cm
3 Total volume of water
= 29070 + 51984
= 81054 cm
3 Base area of the glass tank
= 72 x 57
= 4104 cm
2 Height of water
= 81054 ÷ 4104
= 19.75 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment F
= 34 - 19.75
= 14.25 cm
Drop in the volume of Compartment F
= 57 x 15 x 14.25
= 12183.75 cm
3 Volume of water flowed from F to G in 1 minute
= 12183.75 ÷ 75
≈ 162.5 cm
3 Answer(s): (a) 19.75 cm; (b) 162.5 cm
3