This figure is not drawn to scale. A rectangular glass container 72 cm by 57 cm by 45 cm has 2 compartments, V and W, with a water height of 31 cm in V and 16 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 container 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 31 x 57
= 63612 cm
3 Length of Compartment W
= 72 - 36
= 36 cm
Volume of the water in Compartment W
= 36 x 57 x 16
= 32832 cm
3 Total volume of water
= 63612 + 32832
= 96444 cm
3 Base area of the glass container
= 72 x 57
= 4104 cm
2 Height of water
= 96444 ÷ 4104
= 23.5 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment V
= 31 - 23.5
= 7.5 cm
Drop in the volume of Compartment V
= 57 x 36 x 7.5
= 15390 cm
3 Volume of water flowed from V to W in 1 minute
= 15390 ÷ 90
≈ 171.0 cm
3 Answer(s): (a) 23.5 cm; (b) 171.0 cm
3