This figure is not drawn to scale. A rectangular glass container 75 cm by 54 cm by 49 cm has 2 compartments, T and U, with a water height of 40 cm in T and 13 cm in U. A hole in the slider caused water to leak from T to U. 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 134 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 T to U in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment T
= 37 x 40 x 54
= 79920 cm
3 Length of Compartment U
= 75 - 37
= 38 cm
Volume of the water in Compartment U
= 38 x 54 x 13
= 26676 cm
3 Total volume of water
= 79920 + 26676
= 106596 cm
3 Base area of the glass container
= 75 x 54
= 4050 cm
2 Height of water
= 106596 ÷ 4050
= 26.32 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment T
= 40 - 26.32
= 13.68 cm
Drop in the volume of Compartment T
= 54 x 37 x 13.68
= 27332.64 cm
3 Volume of water flowed from T to U in 1 minute
= 27332.64 ÷ 105
≈ 260.3 cm
3 Answer(s): (a) 26.32 cm; (b) 260.3 cm
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