This figure is not drawn to scale. A rectangular glass tank 70 cm by 52 cm by 48 cm has 2 compartments, A and B, with a water height of 31 cm in A and 17 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 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 A to B in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment A
= 29 x 31 x 52
= 46748 cm
3 Length of Compartment B
= 70 - 29
= 41 cm
Volume of the water in Compartment B
= 41 x 52 x 17
= 36244 cm
3 Total volume of water
= 46748 + 36244
= 82992 cm
3 Base area of the glass tank
= 70 x 52
= 3640 cm
2 Height of water
= 82992 ÷ 3640
= 22.8 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment A
= 31 - 22.8
= 8.2 cm
Drop in the volume of Compartment A
= 52 x 29 x 8.2
= 12365.6 cm
3 Volume of water flowed from A to B in 1 minute
= 12365.6 ÷ 72
≈ 171.7 cm
3 Answer(s): (a) 22.8 cm; (b) 171.7 cm
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