This figure is not drawn to scale. A rectangular glass container 80 cm by 53 cm by 44 cm has 2 compartments, H and J, with a water height of 33 cm in H and 20 cm in J. A hole in the slider caused water to leak from H to J. 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 H to J in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment H
= 20 x 33 x 53
= 34980 cm
3 Length of Compartment J
= 80 - 20
= 60 cm
Volume of the water in Compartment J
= 60 x 53 x 20
= 63600 cm
3 Total volume of water
= 34980 + 63600
= 98580 cm
3 Base area of the glass container
= 80 x 53
= 4240 cm
2 Height of water
= 98580 ÷ 4240
= 23.25 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment H
= 33 - 23.25
= 9.75 cm
Drop in the volume of Compartment H
= 53 x 20 x 9.75
= 10335 cm
3 Volume of water flowed from H to J in 1 minute
= 10335 ÷ 75
≈ 137.8 cm
3 Answer(s): (a) 23.25 cm; (b) 137.8 cm
3