This figure is not drawn to scale. A rectangular glass tank 80 cm by 50 cm by 44 cm has 2 compartments, W and X, with a water height of 35 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 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 W to X in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment W
= 27 x 35 x 50
= 47250 cm
3 Length of Compartment X
= 80 - 27
= 53 cm
Volume of the water in Compartment X
= 53 x 50 x 11
= 29150 cm
3 Total volume of water
= 47250 + 29150
= 76400 cm
3 Base area of the glass tank
= 80 x 50
= 4000 cm
2 Height of water
= 76400 ÷ 4000
= 19.1 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment W
= 35 - 19.1
= 15.9 cm
Drop in the volume of Compartment W
= 50 x 27 x 15.9
= 21465 cm
3 Volume of water flowed from W to X in 1 minute
= 21465 ÷ 105
≈ 204.4 cm
3 Answer(s): (a) 19.1 cm; (b) 204.4 cm
3