This figure is not drawn to scale. A rectangular glass container 70 cm by 59 cm by 47 cm has 2 compartments, W and X, with a water height of 39 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 container 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
= 23 x 39 x 59
= 52923 cm
3 Length of Compartment X
= 70 - 23
= 47 cm
Volume of the water in Compartment X
= 47 x 59 x 11
= 30503 cm
3 Total volume of water
= 52923 + 30503
= 83426 cm
3 Base area of the glass container
= 70 x 59
= 4130 cm
2 Height of water
= 83426 ÷ 4130
= 20.2 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment W
= 39 - 20.2
= 18.8 cm
Drop in the volume of Compartment W
= 59 x 23 x 18.8
= 25511.6 cm
3 Volume of water flowed from W to X in 1 minute
= 25511.6 ÷ 75
≈ 340.2 cm
3 Answer(s): (a) 20.2 cm; (b) 340.2 cm
3