This figure is not drawn to scale. A rectangular glass container 75 cm by 52 cm by 47 cm has 2 compartments, F and G, with a water height of 30 cm in F and 18 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 112 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
= 13 x 30 x 52
= 20280 cm
3 Length of Compartment G
= 75 - 13
= 62 cm
Volume of the water in Compartment G
= 62 x 52 x 18
= 58032 cm
3 Total volume of water
= 20280 + 58032
= 78312 cm
3 Base area of the glass container
= 75 x 52
= 3900 cm
2 Height of water
= 78312 ÷ 3900
= 20.08 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment F
= 30 - 20.08
= 9.92 cm
Drop in the volume of Compartment F
= 52 x 13 x 9.92
= 6705.92 cm
3 Volume of water flowed from F to G in 1 minute
= 6705.92 ÷ 90
≈ 74.5 cm
3 Answer(s): (a) 20.08 cm; (b) 74.5 cm
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