This figure is not drawn to scale. A rectangular glass tank 84 cm by 54 cm by 47 cm has 2 compartments, W and X, with a water height of 30 cm in W and 15 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
= 28 x 30 x 54
= 45360 cm
3 Length of Compartment X
= 84 - 28
= 56 cm
Volume of the water in Compartment X
= 56 x 54 x 15
= 45360 cm
3 Total volume of water
= 45360 + 45360
= 90720 cm
3 Base area of the glass tank
= 84 x 54
= 4536 cm
2 Height of water
= 90720 ÷ 4536
= 20 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment W
= 30 - 20
= 10 cm
Drop in the volume of Compartment W
= 54 x 28 x 10
= 15120 cm
3 Volume of water flowed from W to X in 1 minute
= 15120 ÷ 72
≈ 210.0 cm
3 Answer(s): (a) 20 cm; (b) 210.0 cm
3