This figure is not drawn to scale. A rectangular glass tank 80 cm by 52 cm by 45 cm has 2 compartments, W and X, with a water height of 40 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 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 W to X in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment W
= 40 x 40 x 52
= 83200 cm
3 Length of Compartment X
= 80 - 40
= 40 cm
Volume of the water in Compartment X
= 40 x 52 x 11
= 22880 cm
3 Total volume of water
= 83200 + 22880
= 106080 cm
3 Base area of the glass tank
= 80 x 52
= 4160 cm
2 Height of water
= 106080 ÷ 4160
= 25.5 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment W
= 40 - 25.5
= 14.5 cm
Drop in the volume of Compartment W
= 52 x 40 x 14.5
= 30160 cm
3 Volume of water flowed from W to X in 1 minute
= 30160 ÷ 72
≈ 418.9 cm
3 Answer(s): (a) 25.5 cm; (b) 418.9 cm
3