This figure is not drawn to scale. A rectangular glass tank 90 cm by 60 cm by 46 cm has 2 compartments, V and W, with a water height of 34 cm in V and 13 cm in W. A hole in the slider caused water to leak from V to W. 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 V to W in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment V
= 36 x 34 x 60
= 73440 cm
3 Length of Compartment W
= 90 - 36
= 54 cm
Volume of the water in Compartment W
= 54 x 60 x 13
= 42120 cm
3 Total volume of water
= 73440 + 42120
= 115560 cm
3 Base area of the glass tank
= 90 x 60
= 5400 cm
2 Height of water
= 115560 ÷ 5400
= 21.4 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment V
= 34 - 21.4
= 12.6 cm
Drop in the volume of Compartment V
= 60 x 36 x 12.6
= 27216 cm
3 Volume of water flowed from V to W in 1 minute
= 27216 ÷ 90
≈ 302.4 cm
3 Answer(s): (a) 21.4 cm; (b) 302.4 cm
3