This figure is not drawn to scale. A rectangular glass container 88 cm by 51 cm by 45 cm has 2 compartments, Y and Z, with a water height of 39 cm in Y and 17 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
= 18 x 39 x 51
= 35802 cm
3 Length of Compartment Z
= 88 - 18
= 70 cm
Volume of the water in Compartment Z
= 70 x 51 x 17
= 60690 cm
3 Total volume of water
= 35802 + 60690
= 96492 cm
3 Base area of the glass container
= 88 x 51
= 4488 cm
2 Height of water
= 96492 ÷ 4488
= 21.5 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment Y
= 39 - 21.5
= 17.5 cm
Drop in the volume of Compartment Y
= 51 x 18 x 17.5
= 16065 cm
3 Volume of water flowed from Y to Z in 1 minute
= 16065 ÷ 90
≈ 178.5 cm
3 Answer(s): (a) 21.5 cm; (b) 178.5 cm
3