This figure is not drawn to scale. A rectangular glass container 80 cm by 50 cm by 42 cm has 2 compartments, S and T, with a water height of 37 cm in S and 13 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
= 27 x 37 x 50
= 49950 cm
3 Length of Compartment T
= 80 - 27
= 53 cm
Volume of the water in Compartment T
= 53 x 50 x 13
= 34450 cm
3 Total volume of water
= 49950 + 34450
= 84400 cm
3 Base area of the glass container
= 80 x 50
= 4000 cm
2 Height of water
= 84400 ÷ 4000
= 21.1 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment S
= 37 - 21.1
= 15.9 cm
Drop in the volume of Compartment S
= 50 x 27 x 15.9
= 21465 cm
3 Volume of water flowed from S to T in 1 minute
= 21465 ÷ 105
≈ 204.4 cm
3 Answer(s): (a) 21.1 cm; (b) 204.4 cm
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