This figure is not drawn to scale. A rectangular glass container 75 cm by 51 cm by 49 cm has 2 compartments, F and G, with a water height of 30 cm in F and 10 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 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 F to G in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment F
= 27 x 30 x 51
= 41310 cm
3 Length of Compartment G
= 75 - 27
= 48 cm
Volume of the water in Compartment G
= 48 x 51 x 10
= 24480 cm
3 Total volume of water
= 41310 + 24480
= 65790 cm
3 Base area of the glass container
= 75 x 51
= 3825 cm
2 Height of water
= 65790 ÷ 3825
= 17.2 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment F
= 30 - 17.2
= 12.8 cm
Drop in the volume of Compartment F
= 51 x 27 x 12.8
= 17625.6 cm
3 Volume of water flowed from F to G in 1 minute
= 17625.6 ÷ 105
≈ 167.9 cm
3 Answer(s): (a) 17.2 cm; (b) 167.9 cm
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