This figure is not drawn to scale. A rectangular glass container 70 cm by 55 cm by 41 cm has 2 compartments, F and G, with a water height of 38 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 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
= 35 x 38 x 55
= 73150 cm
3 Length of Compartment G
= 70 - 35
= 35 cm
Volume of the water in Compartment G
= 35 x 55 x 19
= 36575 cm
3 Total volume of water
= 73150 + 36575
= 109725 cm
3 Base area of the glass container
= 70 x 55
= 3850 cm
2 Height of water
= 109725 ÷ 3850
= 28.5 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment F
= 38 - 28.5
= 9.5 cm
Drop in the volume of Compartment F
= 55 x 35 x 9.5
= 18287.5 cm
3 Volume of water flowed from F to G in 1 minute
= 18287.5 ÷ 105
≈ 174.2 cm
3 Answer(s): (a) 28.5 cm; (b) 174.2 cm
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