This figure is not drawn to scale. A rectangular glass container 75 cm by 53 cm by 48 cm has 2 compartments, G and H, with a water height of 39 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 115 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
= 30 x 39 x 53
= 62010 cm
3 Length of Compartment H
= 75 - 30
= 45 cm
Volume of the water in Compartment H
= 45 x 53 x 16
= 38160 cm
3 Total volume of water
= 62010 + 38160
= 100170 cm
3 Base area of the glass container
= 75 x 53
= 3975 cm
2 Height of water
= 100170 ÷ 3975
= 25.2 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment G
= 39 - 25.2
= 13.8 cm
Drop in the volume of Compartment G
= 53 x 30 x 13.8
= 21942 cm
3 Volume of water flowed from G to H in 1 minute
= 21942 ÷ 72
≈ 304.8 cm
3 Answer(s): (a) 25.2 cm; (b) 304.8 cm
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