This figure is not drawn to scale. A rectangular glass container 85 cm by 51 cm by 50 cm has 2 compartments, V and W, with a water height of 33 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 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
= 28 x 33 x 51
= 47124 cm
3 Length of Compartment W
= 85 - 28
= 57 cm
Volume of the water in Compartment W
= 57 x 51 x 16
= 46512 cm
3 Total volume of water
= 47124 + 46512
= 93636 cm
3 Base area of the glass container
= 85 x 51
= 4335 cm
2 Height of water
= 93636 ÷ 4335
= 21.6 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment V
= 33 - 21.6
= 11.4 cm
Drop in the volume of Compartment V
= 51 x 28 x 11.4
= 16279.2 cm
3 Volume of water flowed from V to W in 1 minute
= 16279.2 ÷ 72
≈ 226.1 cm
3 Answer(s): (a) 21.6 cm; (b) 226.1 cm
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