This figure is not drawn to scale. A rectangular glass container 87 cm by 52 cm by 43 cm has 2 compartments, F and G, with a water height of 35 cm in F and 20 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 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 F to G in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment F
= 29 x 35 x 52
= 52780 cm
3 Length of Compartment G
= 87 - 29
= 58 cm
Volume of the water in Compartment G
= 58 x 52 x 20
= 60320 cm
3 Total volume of water
= 52780 + 60320
= 113100 cm
3 Base area of the glass container
= 87 x 52
= 4524 cm
2 Height of water
= 113100 ÷ 4524
= 25 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment F
= 35 - 25
= 10 cm
Drop in the volume of Compartment F
= 52 x 29 x 10
= 15080 cm
3 Volume of water flowed from F to G in 1 minute
= 15080 ÷ 72
≈ 209.4 cm
3 Answer(s): (a) 25 cm; (b) 209.4 cm
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