This figure is not drawn to scale. A rectangular glass container 88 cm by 51 cm by 41 cm has 2 compartments, S and T, with a water height of 36 cm in S and 14 cm in T. A hole in the slider caused water to leak from S to T. 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 S to T in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment S
= 37 x 36 x 51
= 67932 cm
3 Length of Compartment T
= 88 - 37
= 51 cm
Volume of the water in Compartment T
= 51 x 51 x 14
= 36414 cm
3 Total volume of water
= 67932 + 36414
= 104346 cm
3 Base area of the glass container
= 88 x 51
= 4488 cm
2 Height of water
= 104346 ÷ 4488
= 23.25 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment S
= 36 - 23.25
= 12.75 cm
Drop in the volume of Compartment S
= 51 x 37 x 12.75
= 24059.25 cm
3 Volume of water flowed from S to T in 1 minute
= 24059.25 ÷ 105
≈ 229.1 cm
3 Answer(s): (a) 23.25 cm; (b) 229.1 cm
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