This figure is not drawn to scale. A rectangular glass container 80 cm by 54 cm by 42 cm has 2 compartments, G and H, with a water height of 33 cm in G and 17 cm in H. A hole in the slider caused water to leak from G to H. 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 134 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 G to H in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment G
= 31 x 33 x 54
= 55242 cm
3 Length of Compartment H
= 80 - 31
= 49 cm
Volume of the water in Compartment H
= 49 x 54 x 17
= 44982 cm
3 Total volume of water
= 55242 + 44982
= 100224 cm
3 Base area of the glass container
= 80 x 54
= 4320 cm
2 Height of water
= 100224 ÷ 4320
= 23.2 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment G
= 33 - 23.2
= 9.8 cm
Drop in the volume of Compartment G
= 54 x 31 x 9.8
= 16405.2 cm
3 Volume of water flowed from G to H in 1 minute
= 16405.2 ÷ 105
≈ 156.2 cm
3 Answer(s): (a) 23.2 cm; (b) 156.2 cm
3