This figure is not drawn to scale. A rectangular glass tank 72 cm by 54 cm by 41 cm has 2 compartments, E and F, with a water height of 34 cm in E and 11 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 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 E to F in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment E
= 36 x 34 x 54
= 66096 cm
3 Length of Compartment F
= 72 - 36
= 36 cm
Volume of the water in Compartment F
= 36 x 54 x 11
= 21384 cm
3 Total volume of water
= 66096 + 21384
= 87480 cm
3 Base area of the glass tank
= 72 x 54
= 3888 cm
2 Height of water
= 87480 ÷ 3888
= 22.5 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment E
= 34 - 22.5
= 11.5 cm
Drop in the volume of Compartment E
= 54 x 36 x 11.5
= 22356 cm
3 Volume of water flowed from E to F in 1 minute
= 22356 ÷ 105
≈ 212.9 cm
3 Answer(s): (a) 22.5 cm; (b) 212.9 cm
3