This figure is not drawn to scale. A rectangular glass container 85 cm by 57 cm by 48 cm has 2 compartments, J and K, with a water height of 40 cm in J and 10 cm in K. A hole in the slider caused water to leak from J to K. 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 J to K in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment J
= 17 x 40 x 57
= 38760 cm
3 Length of Compartment K
= 85 - 17
= 68 cm
Volume of the water in Compartment K
= 68 x 57 x 10
= 38760 cm
3 Total volume of water
= 38760 + 38760
= 77520 cm
3 Base area of the glass container
= 85 x 57
= 4845 cm
2 Height of water
= 77520 ÷ 4845
= 16 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment J
= 40 - 16
= 24 cm
Drop in the volume of Compartment J
= 57 x 17 x 24
= 23256 cm
3 Volume of water flowed from J to K in 1 minute
= 23256 ÷ 90
≈ 258.4 cm
3 Answer(s): (a) 16 cm; (b) 258.4 cm
3