This figure is not drawn to scale. A rectangular glass container 90 cm by 60 cm by 41 cm has 2 compartments, E and F, with a water height of 37 cm in E and 14 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 115 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
= 36 x 37 x 60
= 79920 cm
3 Length of Compartment F
= 90 - 36
= 54 cm
Volume of the water in Compartment F
= 54 x 60 x 14
= 45360 cm
3 Total volume of water
= 79920 + 45360
= 125280 cm
3 Base area of the glass container
= 90 x 60
= 5400 cm
2 Height of water
= 125280 ÷ 5400
= 23.2 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment E
= 37 - 23.2
= 13.8 cm
Drop in the volume of Compartment E
= 60 x 36 x 13.8
= 29808 cm
3 Volume of water flowed from E to F in 1 minute
= 29808 ÷ 72
≈ 414.0 cm
3 Answer(s): (a) 23.2 cm; (b) 414.0 cm
3