This figure is not drawn to scale. A rectangular glass container 75 cm by 51 cm by 45 cm has 2 compartments, E and F, with a water height of 37 cm in E and 13 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
= 39 x 37 x 51
= 73593 cm
3 Length of Compartment F
= 75 - 39
= 36 cm
Volume of the water in Compartment F
= 36 x 51 x 13
= 23868 cm
3 Total volume of water
= 73593 + 23868
= 97461 cm
3 Base area of the glass container
= 75 x 51
= 3825 cm
2 Height of water
= 97461 ÷ 3825
= 25.48 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment E
= 37 - 25.48
= 11.52 cm
Drop in the volume of Compartment E
= 51 x 39 x 11.52
= 22913.28 cm
3 Volume of water flowed from E to F in 1 minute
= 22913.28 ÷ 75
≈ 305.5 cm
3 Answer(s): (a) 25.48 cm; (b) 305.5 cm
3