This figure is not drawn to scale. A rectangular glass container 70 cm by 51 cm by 44 cm has 2 compartments, F and G, with a water height of 40 cm in F and 19 cm in G. A hole in the slider caused water to leak from F to G. 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 112 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 F to G in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment F
= 34 x 40 x 51
= 69360 cm
3 Length of Compartment G
= 70 - 34
= 36 cm
Volume of the water in Compartment G
= 36 x 51 x 19
= 34884 cm
3 Total volume of water
= 69360 + 34884
= 104244 cm
3 Base area of the glass container
= 70 x 51
= 3570 cm
2 Height of water
= 104244 ÷ 3570
= 29.2 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment F
= 40 - 29.2
= 10.8 cm
Drop in the volume of Compartment F
= 51 x 34 x 10.8
= 18727.2 cm
3 Volume of water flowed from F to G in 1 minute
= 18727.2 ÷ 90
≈ 208.1 cm
3 Answer(s): (a) 29.2 cm; (b) 208.1 cm
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