This figure is not drawn to scale. A rectangular glass tank 80 cm by 57 cm by 45 cm has 2 compartments, V and W, with a water height of 33 cm in V and 11 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
= 16 x 33 x 57
= 30096 cm
3 Length of Compartment W
= 80 - 16
= 64 cm
Volume of the water in Compartment W
= 64 x 57 x 11
= 40128 cm
3 Total volume of water
= 30096 + 40128
= 70224 cm
3 Base area of the glass tank
= 80 x 57
= 4560 cm
2 Height of water
= 70224 ÷ 4560
= 15.4 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment V
= 33 - 15.4
= 17.6 cm
Drop in the volume of Compartment V
= 57 x 16 x 17.6
= 16051.2 cm
3 Volume of water flowed from V to W in 1 minute
= 16051.2 ÷ 90
≈ 178.3 cm
3 Answer(s): (a) 15.4 cm; (b) 178.3 cm
3