This figure is not drawn to scale. A rectangular glass container 88 cm by 56 cm by 47 cm has 2 compartments, E and F, with a water height of 37 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 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 E to F in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment E
= 17 x 37 x 56
= 35224 cm
3 Length of Compartment F
= 88 - 17
= 71 cm
Volume of the water in Compartment F
= 71 x 56 x 15
= 59640 cm
3 Total volume of water
= 35224 + 59640
= 94864 cm
3 Base area of the glass container
= 88 x 56
= 4928 cm
2 Height of water
= 94864 ÷ 4928
= 19.25 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment E
= 37 - 19.25
= 17.75 cm
Drop in the volume of Compartment E
= 56 x 17 x 17.75
= 16898 cm
3 Volume of water flowed from E to F in 1 minute
= 16898 ÷ 90
≈ 187.8 cm
3 Answer(s): (a) 19.25 cm; (b) 187.8 cm
3