This figure is not drawn to scale. A rectangular glass container 80 cm by 60 cm by 40 cm has 2 compartments, E and F, with a water height of 31 cm in E and 15 cm in F. A hole in the slider caused water to leak from E to F. 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 E to F in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment E
= 25 x 31 x 60
= 46500 cm
3 Length of Compartment F
= 80 - 25
= 55 cm
Volume of the water in Compartment F
= 55 x 60 x 15
= 49500 cm
3 Total volume of water
= 46500 + 49500
= 96000 cm
3 Base area of the glass container
= 80 x 60
= 4800 cm
2 Height of water
= 96000 ÷ 4800
= 20 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment E
= 31 - 20
= 11 cm
Drop in the volume of Compartment E
= 60 x 25 x 11
= 16500 cm
3 Volume of water flowed from E to F in 1 minute
= 16500 ÷ 75
≈ 220.0 cm
3 Answer(s): (a) 20 cm; (b) 220.0 cm
3