This figure is not drawn to scale. A rectangular glass container 84 cm by 51 cm by 41 cm has 2 compartments, E and F, with a water height of 38 cm in E and 10 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 134 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
= 24 x 38 x 51
= 46512 cm
3 Length of Compartment F
= 84 - 24
= 60 cm
Volume of the water in Compartment F
= 60 x 51 x 10
= 30600 cm
3 Total volume of water
= 46512 + 30600
= 77112 cm
3 Base area of the glass container
= 84 x 51
= 4284 cm
2 Height of water
= 77112 ÷ 4284
= 18 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment E
= 38 - 18
= 20 cm
Drop in the volume of Compartment E
= 51 x 24 x 20
= 24480 cm
3 Volume of water flowed from E to F in 1 minute
= 24480 ÷ 105
≈ 233.1 cm
3 Answer(s): (a) 18 cm; (b) 233.1 cm
3