This figure is not drawn to scale. A rectangular glass container 88 cm by 52 cm by 44 cm has 2 compartments, G and H, with a water height of 35 cm in G and 16 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
= 22 x 35 x 52
= 40040 cm
3 Length of Compartment H
= 88 - 22
= 66 cm
Volume of the water in Compartment H
= 66 x 52 x 16
= 54912 cm
3 Total volume of water
= 40040 + 54912
= 94952 cm
3 Base area of the glass container
= 88 x 52
= 4576 cm
2 Height of water
= 94952 ÷ 4576
= 20.75 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment G
= 35 - 20.75
= 14.25 cm
Drop in the volume of Compartment G
= 52 x 22 x 14.25
= 16302 cm
3 Volume of water flowed from G to H in 1 minute
= 16302 ÷ 105
≈ 155.3 cm
3 Answer(s): (a) 20.75 cm; (b) 155.3 cm
3