This figure is not drawn to scale. A rectangular glass container 80 cm by 58 cm by 46 cm has 2 compartments, E and F, with a water height of 31 cm in E and 17 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
= 18 x 31 x 58
= 32364 cm
3 Length of Compartment F
= 80 - 18
= 62 cm
Volume of the water in Compartment F
= 62 x 58 x 17
= 61132 cm
3 Total volume of water
= 32364 + 61132
= 93496 cm
3 Base area of the glass container
= 80 x 58
= 4640 cm
2 Height of water
= 93496 ÷ 4640
= 20.15 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment E
= 31 - 20.15
= 10.85 cm
Drop in the volume of Compartment E
= 58 x 18 x 10.85
= 11327.4 cm
3 Volume of water flowed from E to F in 1 minute
= 11327.4 ÷ 90
≈ 125.9 cm
3 Answer(s): (a) 20.15 cm; (b) 125.9 cm
3