This figure is not drawn to scale. A rectangular glass container 85 cm by 57 cm by 49 cm has 2 compartments, S and T, with a water height of 33 cm in S and 16 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 114 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
= 13 x 33 x 57
= 24453 cm
3 Length of Compartment T
= 85 - 13
= 72 cm
Volume of the water in Compartment T
= 72 x 57 x 16
= 65664 cm
3 Total volume of water
= 24453 + 65664
= 90117 cm
3 Base area of the glass container
= 85 x 57
= 4845 cm
2 Height of water
= 90117 ÷ 4845
= 18.6 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment S
= 33 - 18.6
= 14.4 cm
Drop in the volume of Compartment S
= 57 x 13 x 14.4
= 10670.4 cm
3 Volume of water flowed from S to T in 1 minute
= 10670.4 ÷ 75
≈ 142.3 cm
3 Answer(s): (a) 18.6 cm; (b) 142.3 cm
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