This figure is not drawn to scale. A rectangular glass container 90 cm by 56 cm by 46 cm has 2 compartments, Y and Z, with a water height of 33 cm in Y and 15 cm in Z. A hole in the slider caused water to leak from Y to Z. 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 112 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 Y to Z in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment Y
= 10 x 33 x 56
= 18480 cm
3 Length of Compartment Z
= 90 - 10
= 80 cm
Volume of the water in Compartment Z
= 80 x 56 x 15
= 67200 cm
3 Total volume of water
= 18480 + 67200
= 85680 cm
3 Base area of the glass container
= 90 x 56
= 5040 cm
2 Height of water
= 85680 ÷ 5040
= 17 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment Y
= 33 - 17
= 16 cm
Drop in the volume of Compartment Y
= 56 x 10 x 16
= 8960 cm
3 Volume of water flowed from Y to Z in 1 minute
= 8960 ÷ 90
≈ 99.6 cm
3 Answer(s): (a) 17 cm; (b) 99.6 cm
3