This figure is not drawn to scale. A rectangular glass container 85 cm by 55 cm by 45 cm has 2 compartments, V and W, with a water height of 37 cm in V and 15 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
= 17 x 37 x 55
= 34595 cm
3 Length of Compartment W
= 85 - 17
= 68 cm
Volume of the water in Compartment W
= 68 x 55 x 15
= 56100 cm
3 Total volume of water
= 34595 + 56100
= 90695 cm
3 Base area of the glass container
= 85 x 55
= 4675 cm
2 Height of water
= 90695 ÷ 4675
= 19.4 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment V
= 37 - 19.4
= 17.6 cm
Drop in the volume of Compartment V
= 55 x 17 x 17.6
= 16456 cm
3 Volume of water flowed from V to W in 1 minute
= 16456 ÷ 72
≈ 228.6 cm
3 Answer(s): (a) 19.4 cm; (b) 228.6 cm
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