This figure is not drawn to scale. A rectangular glass container 84 cm by 60 cm by 42 cm has 2 compartments, F and G, with a water height of 36 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
= 13 x 36 x 60
= 28080 cm
3 Length of Compartment G
= 84 - 13
= 71 cm
Volume of the water in Compartment G
= 71 x 60 x 15
= 63900 cm
3 Total volume of water
= 28080 + 63900
= 91980 cm
3 Base area of the glass container
= 84 x 60
= 5040 cm
2 Height of water
= 91980 ÷ 5040
= 18.25 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment F
= 36 - 18.25
= 17.75 cm
Drop in the volume of Compartment F
= 60 x 13 x 17.75
= 13845 cm
3 Volume of water flowed from F to G in 1 minute
= 13845 ÷ 75
≈ 184.6 cm
3 Answer(s): (a) 18.25 cm; (b) 184.6 cm
3