This figure is not drawn to scale. A rectangular glass tank 80 cm by 56 cm by 46 cm has 2 compartments, F and G, with a water height of 39 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 tank 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
= 12 x 39 x 56
= 26208 cm
3 Length of Compartment G
= 80 - 12
= 68 cm
Volume of the water in Compartment G
= 68 x 56 x 10
= 38080 cm
3 Total volume of water
= 26208 + 38080
= 64288 cm
3 Base area of the glass tank
= 80 x 56
= 4480 cm
2 Height of water
= 64288 ÷ 4480
= 14.35 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment F
= 39 - 14.35
= 24.65 cm
Drop in the volume of Compartment F
= 56 x 12 x 24.65
= 16564.8 cm
3 Volume of water flowed from F to G in 1 minute
= 16564.8 ÷ 105
≈ 157.8 cm
3 Answer(s): (a) 14.35 cm; (b) 157.8 cm
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