This figure is not drawn to scale. A rectangular glass container 75 cm by 58 cm by 50 cm has 2 compartments, H and J, with a water height of 39 cm in H and 16 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
= 24 x 39 x 58
= 54288 cm
3 Length of Compartment J
= 75 - 24
= 51 cm
Volume of the water in Compartment J
= 51 x 58 x 16
= 47328 cm
3 Total volume of water
= 54288 + 47328
= 101616 cm
3 Base area of the glass container
= 75 x 58
= 4350 cm
2 Height of water
= 101616 ÷ 4350
= 23.36 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment H
= 39 - 23.36
= 15.64 cm
Drop in the volume of Compartment H
= 58 x 24 x 15.64
= 21770.88 cm
3 Volume of water flowed from H to J in 1 minute
= 21770.88 ÷ 90
≈ 241.9 cm
3 Answer(s): (a) 23.36 cm; (b) 241.9 cm
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