This figure is not drawn to scale. A rectangular glass container 74 cm by 52 cm by 48 cm has 2 compartments, F and G, with a water height of 35 cm in F and 11 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
= 37 x 35 x 52
= 67340 cm
3 Length of Compartment G
= 74 - 37
= 37 cm
Volume of the water in Compartment G
= 37 x 52 x 11
= 21164 cm
3 Total volume of water
= 67340 + 21164
= 88504 cm
3 Base area of the glass container
= 74 x 52
= 3848 cm
2 Height of water
= 88504 ÷ 3848
= 23 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment F
= 35 - 23
= 12 cm
Drop in the volume of Compartment F
= 52 x 37 x 12
= 23088 cm
3 Volume of water flowed from F to G in 1 minute
= 23088 ÷ 72
≈ 320.7 cm
3 Answer(s): (a) 23 cm; (b) 320.7 cm
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