This figure is not drawn to scale. A rectangular glass container 90 cm by 52 cm by 45 cm has 2 compartments, T and U, with a water height of 35 cm in T and 16 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 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 T to U in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment T
= 36 x 35 x 52
= 65520 cm
3 Length of Compartment U
= 90 - 36
= 54 cm
Volume of the water in Compartment U
= 54 x 52 x 16
= 44928 cm
3 Total volume of water
= 65520 + 44928
= 110448 cm
3 Base area of the glass container
= 90 x 52
= 4680 cm
2 Height of water
= 110448 ÷ 4680
= 23.6 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment T
= 35 - 23.6
= 11.4 cm
Drop in the volume of Compartment T
= 52 x 36 x 11.4
= 21340.8 cm
3 Volume of water flowed from T to U in 1 minute
= 21340.8 ÷ 72
≈ 296.4 cm
3 Answer(s): (a) 23.6 cm; (b) 296.4 cm
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