This figure is not drawn to scale. A rectangular glass tank 84 cm by 57 cm by 50 cm has 2 compartments, W and X, with a water height of 32 cm in W and 11 cm in X. A hole in the slider caused water to leak from W to X. 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 114 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 W to X in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment W
= 40 x 32 x 57
= 72960 cm
3 Length of Compartment X
= 84 - 40
= 44 cm
Volume of the water in Compartment X
= 44 x 57 x 11
= 27588 cm
3 Total volume of water
= 72960 + 27588
= 100548 cm
3 Base area of the glass tank
= 84 x 57
= 4788 cm
2 Height of water
= 100548 ÷ 4788
= 21 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment W
= 32 - 21
= 11 cm
Drop in the volume of Compartment W
= 57 x 40 x 11
= 25080 cm
3 Volume of water flowed from W to X in 1 minute
= 25080 ÷ 75
≈ 334.4 cm
3 Answer(s): (a) 21 cm; (b) 334.4 cm
3