This figure is not drawn to scale. A rectangular glass container 72 cm by 56 cm by 40 cm has 2 compartments, F and G, with a water height of 30 cm in F and 12 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 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 F to G in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment F
= 27 x 30 x 56
= 45360 cm
3 Length of Compartment G
= 72 - 27
= 45 cm
Volume of the water in Compartment G
= 45 x 56 x 12
= 30240 cm
3 Total volume of water
= 45360 + 30240
= 75600 cm
3 Base area of the glass container
= 72 x 56
= 4032 cm
2 Height of water
= 75600 ÷ 4032
= 18.75 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment F
= 30 - 18.75
= 11.25 cm
Drop in the volume of Compartment F
= 56 x 27 x 11.25
= 17010 cm
3 Volume of water flowed from F to G in 1 minute
= 17010 ÷ 90
≈ 189.0 cm
3 Answer(s): (a) 18.75 cm; (b) 189.0 cm
3