This figure is not drawn to scale. A rectangular glass container 90 cm by 59 cm by 47 cm has 2 compartments, E and F, with a water height of 33 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 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 E to F in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment E
= 36 x 33 x 59
= 70092 cm
3 Length of Compartment F
= 90 - 36
= 54 cm
Volume of the water in Compartment F
= 54 x 59 x 16
= 50976 cm
3 Total volume of water
= 70092 + 50976
= 121068 cm
3 Base area of the glass container
= 90 x 59
= 5310 cm
2 Height of water
= 121068 ÷ 5310
= 22.8 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment E
= 33 - 22.8
= 10.2 cm
Drop in the volume of Compartment E
= 59 x 36 x 10.2
= 21664.8 cm
3 Volume of water flowed from E to F in 1 minute
= 21664.8 ÷ 90
≈ 240.7 cm
3 Answer(s): (a) 22.8 cm; (b) 240.7 cm
3