This figure is not drawn to scale. A rectangular glass tank 90 cm by 54 cm by 41 cm has 2 compartments, A and B, with a water height of 38 cm in A and 18 cm in B. A hole in the slider caused water to leak from A to B. 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 A to B in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment A
= 27 x 38 x 54
= 55404 cm
3 Length of Compartment B
= 90 - 27
= 63 cm
Volume of the water in Compartment B
= 63 x 54 x 18
= 61236 cm
3 Total volume of water
= 55404 + 61236
= 116640 cm
3 Base area of the glass tank
= 90 x 54
= 4860 cm
2 Height of water
= 116640 ÷ 4860
= 24 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment A
= 38 - 24
= 14 cm
Drop in the volume of Compartment A
= 54 x 27 x 14
= 20412 cm
3 Volume of water flowed from A to B in 1 minute
= 20412 ÷ 105
≈ 194.4 cm
3 Answer(s): (a) 24 cm; (b) 194.4 cm
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