This figure is not drawn to scale. A rectangular glass tank 80 cm by 55 cm by 46 cm has 2 compartments, U and V, with a water height of 38 cm in U and 12 cm in V. A hole in the slider caused water to leak from U to V. 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 U to V in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment U
= 16 x 38 x 55
= 33440 cm
3 Length of Compartment V
= 80 - 16
= 64 cm
Volume of the water in Compartment V
= 64 x 55 x 12
= 42240 cm
3 Total volume of water
= 33440 + 42240
= 75680 cm
3 Base area of the glass tank
= 80 x 55
= 4400 cm
2 Height of water
= 75680 ÷ 4400
= 17.2 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment U
= 38 - 17.2
= 20.8 cm
Drop in the volume of Compartment U
= 55 x 16 x 20.8
= 18304 cm
3 Volume of water flowed from U to V in 1 minute
= 18304 ÷ 90
≈ 203.4 cm
3 Answer(s): (a) 17.2 cm; (b) 203.4 cm
3