This figure is not drawn to scale. A rectangular glass container 75 cm by 55 cm by 40 cm has 2 compartments, Y and Z, with a water height of 34 cm in Y and 16 cm in Z. A hole in the slider caused water to leak from Y to Z. 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 Y to Z in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment Y
= 16 x 34 x 55
= 29920 cm
3 Length of Compartment Z
= 75 - 16
= 59 cm
Volume of the water in Compartment Z
= 59 x 55 x 16
= 51920 cm
3 Total volume of water
= 29920 + 51920
= 81840 cm
3 Base area of the glass container
= 75 x 55
= 4125 cm
2 Height of water
= 81840 ÷ 4125
= 19.84 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment Y
= 34 - 19.84
= 14.16 cm
Drop in the volume of Compartment Y
= 55 x 16 x 14.16
= 12460.8 cm
3 Volume of water flowed from Y to Z in 1 minute
= 12460.8 ÷ 72
≈ 173.1 cm
3 Answer(s): (a) 19.84 cm; (b) 173.1 cm
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