This figure is not drawn to scale. A rectangular glass tank 75 cm by 60 cm by 43 cm has 2 compartments, B and C, with a water height of 30 cm in B and 14 cm in C. A hole in the slider caused water to leak from B to C. 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 115 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 B to C in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment B
= 12 x 30 x 60
= 21600 cm
3 Length of Compartment C
= 75 - 12
= 63 cm
Volume of the water in Compartment C
= 63 x 60 x 14
= 52920 cm
3 Total volume of water
= 21600 + 52920
= 74520 cm
3 Base area of the glass tank
= 75 x 60
= 4500 cm
2 Height of water
= 74520 ÷ 4500
= 16.56 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment B
= 30 - 16.56
= 13.44 cm
Drop in the volume of Compartment B
= 60 x 12 x 13.44
= 9676.8 cm
3 Volume of water flowed from B to C in 1 minute
= 9676.8 ÷ 72
≈ 134.4 cm
3 Answer(s): (a) 16.56 cm; (b) 134.4 cm
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