This figure is not drawn to scale. A rectangular glass container 70 cm by 52 cm by 47 cm has 2 compartments, S and T, with a water height of 31 cm in S and 18 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 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 S to T in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment S
= 28 x 31 x 52
= 45136 cm
3 Length of Compartment T
= 70 - 28
= 42 cm
Volume of the water in Compartment T
= 42 x 52 x 18
= 39312 cm
3 Total volume of water
= 45136 + 39312
= 84448 cm
3 Base area of the glass container
= 70 x 52
= 3640 cm
2 Height of water
= 84448 ÷ 3640
= 23.2 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment S
= 31 - 23.2
= 7.8 cm
Drop in the volume of Compartment S
= 52 x 28 x 7.8
= 11356.8 cm
3 Volume of water flowed from S to T in 1 minute
= 11356.8 ÷ 90
≈ 126.2 cm
3 Answer(s): (a) 23.2 cm; (b) 126.2 cm
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