This figure is not drawn to scale. A rectangular glass container 80 cm by 50 cm by 50 cm has 2 compartments, F and G, with a water height of 39 cm in F and 15 cm in G. A hole in the slider caused water to leak from F to G. 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 F to G in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment F
= 35 x 39 x 50
= 68250 cm
3 Length of Compartment G
= 80 - 35
= 45 cm
Volume of the water in Compartment G
= 45 x 50 x 15
= 33750 cm
3 Total volume of water
= 68250 + 33750
= 102000 cm
3 Base area of the glass container
= 80 x 50
= 4000 cm
2 Height of water
= 102000 ÷ 4000
= 25.5 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment F
= 39 - 25.5
= 13.5 cm
Drop in the volume of Compartment F
= 50 x 35 x 13.5
= 23625 cm
3 Volume of water flowed from F to G in 1 minute
= 23625 ÷ 75
≈ 315.0 cm
3 Answer(s): (a) 25.5 cm; (b) 315.0 cm
3