This figure is not drawn to scale. A rectangular glass container 78 cm by 50 cm by 49 cm has 2 compartments, W and X, with a water height of 36 cm in W and 10 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
= 39 x 36 x 50
= 70200 cm
3 Length of Compartment X
= 78 - 39
= 39 cm
Volume of the water in Compartment X
= 39 x 50 x 10
= 19500 cm
3 Total volume of water
= 70200 + 19500
= 89700 cm
3 Base area of the glass container
= 78 x 50
= 3900 cm
2 Height of water
= 89700 ÷ 3900
= 23 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment W
= 36 - 23
= 13 cm
Drop in the volume of Compartment W
= 50 x 39 x 13
= 25350 cm
3 Volume of water flowed from W to X in 1 minute
= 25350 ÷ 75
≈ 338.0 cm
3 Answer(s): (a) 23 cm; (b) 338.0 cm
3