This figure is not drawn to scale. A rectangular glass container 70 cm by 53 cm by 40 cm has 2 compartments, V and W, with a water height of 35 cm in V and 20 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 115 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
= 14 x 35 x 53
= 25970 cm
3 Length of Compartment W
= 70 - 14
= 56 cm
Volume of the water in Compartment W
= 56 x 53 x 20
= 59360 cm
3 Total volume of water
= 25970 + 59360
= 85330 cm
3 Base area of the glass container
= 70 x 53
= 3710 cm
2 Height of water
= 85330 ÷ 3710
= 23 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment V
= 35 - 23
= 12 cm
Drop in the volume of Compartment V
= 53 x 14 x 12
= 8904 cm
3 Volume of water flowed from V to W in 1 minute
= 8904 ÷ 72
≈ 123.7 cm
3 Answer(s): (a) 23 cm; (b) 123.7 cm
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