This figure is not drawn to scale. A rectangular glass container 90 cm by 55 cm by 50 cm has 2 compartments, E and F, with a water height of 34 cm in E and 16 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
= 13 x 34 x 55
= 24310 cm
3 Length of Compartment F
= 90 - 13
= 77 cm
Volume of the water in Compartment F
= 77 x 55 x 16
= 67760 cm
3 Total volume of water
= 24310 + 67760
= 92070 cm
3 Base area of the glass container
= 90 x 55
= 4950 cm
2 Height of water
= 92070 ÷ 4950
= 18.6 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment E
= 34 - 18.6
= 15.4 cm
Drop in the volume of Compartment E
= 55 x 13 x 15.4
= 11011 cm
3 Volume of water flowed from E to F in 1 minute
= 11011 ÷ 75
≈ 146.8 cm
3 Answer(s): (a) 18.6 cm; (b) 146.8 cm
3