This figure is not drawn to scale. A rectangular glass container 78 cm by 56 cm by 48 cm has 2 compartments, W and X, with a water height of 30 cm in W and 14 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 30 x 56
= 65520 cm
3 Length of Compartment X
= 78 - 39
= 39 cm
Volume of the water in Compartment X
= 39 x 56 x 14
= 30576 cm
3 Total volume of water
= 65520 + 30576
= 96096 cm
3 Base area of the glass container
= 78 x 56
= 4368 cm
2 Height of water
= 96096 ÷ 4368
= 22 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment W
= 30 - 22
= 8 cm
Drop in the volume of Compartment W
= 56 x 39 x 8
= 17472 cm
3 Volume of water flowed from W to X in 1 minute
= 17472 ÷ 75
≈ 233 cm
3 Answer(s): (a) 22 cm; (b) 233 cm
3