This figure is not drawn to scale. A rectangular glass container 75 cm by 50 cm by 42 cm has 2 compartments, H and J, with a water height of 39 cm in H and 15 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 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 H to J in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment H
= 33 x 39 x 50
= 64350 cm
3 Length of Compartment J
= 75 - 33
= 42 cm
Volume of the water in Compartment J
= 42 x 50 x 15
= 31500 cm
3 Total volume of water
= 64350 + 31500
= 95850 cm
3 Base area of the glass container
= 75 x 50
= 3750 cm
2 Height of water
= 95850 ÷ 3750
= 25.56 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment H
= 39 - 25.56
= 13.44 cm
Drop in the volume of Compartment H
= 50 x 33 x 13.44
= 22176 cm
3 Volume of water flowed from H to J in 1 minute
= 22176 ÷ 90
≈ 246.4 cm
3 Answer(s): (a) 25.56 cm; (b) 246.4 cm
3