This figure is not drawn to scale. A rectangular glass container 75 cm by 60 cm by 46 cm has 2 compartments, L and M, with a water height of 38 cm in L and 19 cm in M. A hole in the slider caused water to leak from L to M. 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 L to M in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment L
= 18 x 38 x 60
= 41040 cm
3 Length of Compartment M
= 75 - 18
= 57 cm
Volume of the water in Compartment M
= 57 x 60 x 19
= 64980 cm
3 Total volume of water
= 41040 + 64980
= 106020 cm
3 Base area of the glass container
= 75 x 60
= 4500 cm
2 Height of water
= 106020 ÷ 4500
= 23.56 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment L
= 38 - 23.56
= 14.44 cm
Drop in the volume of Compartment L
= 60 x 18 x 14.44
= 15595.2 cm
3 Volume of water flowed from L to M in 1 minute
= 15595.2 ÷ 105
≈ 148.5 cm
3 Answer(s): (a) 23.56 cm; (b) 148.5 cm
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