This figure is not drawn to scale. A rectangular glass container 75 cm by 54 cm by 45 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
= 32 x 34 x 54
= 58752 cm
3 Length of Compartment Z
= 75 - 32
= 43 cm
Volume of the water in Compartment Z
= 43 x 54 x 16
= 37152 cm
3 Total volume of water
= 58752 + 37152
= 95904 cm
3 Base area of the glass container
= 75 x 54
= 4050 cm
2 Height of water
= 95904 ÷ 4050
= 23.68 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment Y
= 34 - 23.68
= 10.32 cm
Drop in the volume of Compartment Y
= 54 x 32 x 10.32
= 17832.96 cm
3 Volume of water flowed from Y to Z in 1 minute
= 17832.96 ÷ 72
≈ 247.7 cm
3 Answer(s): (a) 23.68 cm; (b) 247.7 cm
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