This figure is not drawn to scale. A rectangular glass container 80 cm by 54 cm by 45 cm has 2 compartments, T and U, with a water height of 33 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
= 12 x 33 x 54
= 21384 cm
3 Length of Compartment U
= 80 - 12
= 68 cm
Volume of the water in Compartment U
= 68 x 54 x 13
= 47736 cm
3 Total volume of water
= 21384 + 47736
= 69120 cm
3 Base area of the glass container
= 80 x 54
= 4320 cm
2 Height of water
= 69120 ÷ 4320
= 16 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment T
= 33 - 16
= 17 cm
Drop in the volume of Compartment T
= 54 x 12 x 17
= 11016 cm
3 Volume of water flowed from T to U in 1 minute
= 11016 ÷ 105
≈ 104.9 cm
3 Answer(s): (a) 16 cm; (b) 104.9 cm
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