This figure is not drawn to scale. A rectangular glass container 75 cm by 56 cm by 41 cm has 2 compartments, F and G, with a water height of 31 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 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
= 33 x 31 x 56
= 57288 cm
3 Length of Compartment G
= 75 - 33
= 42 cm
Volume of the water in Compartment G
= 42 x 56 x 20
= 47040 cm
3 Total volume of water
= 57288 + 47040
= 104328 cm
3 Base area of the glass container
= 75 x 56
= 4200 cm
2 Height of water
= 104328 ÷ 4200
= 24.84 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment F
= 31 - 24.84
= 6.16 cm
Drop in the volume of Compartment F
= 56 x 33 x 6.16
= 11383.68 cm
3 Volume of water flowed from F to G in 1 minute
= 11383.68 ÷ 105
≈ 108.4 cm
3 Answer(s): (a) 24.84 cm; (b) 108.4 cm
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