This figure is not drawn to scale. A rectangular glass container 75 cm by 57 cm by 49 cm has 2 compartments, S and T, with a water height of 38 cm in S and 20 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
= 32 x 38 x 57
= 69312 cm
3 Length of Compartment T
= 75 - 32
= 43 cm
Volume of the water in Compartment T
= 43 x 57 x 20
= 49020 cm
3 Total volume of water
= 69312 + 49020
= 118332 cm
3 Base area of the glass container
= 75 x 57
= 4275 cm
2 Height of water
= 118332 ÷ 4275
= 27.68 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment S
= 38 - 27.68
= 10.32 cm
Drop in the volume of Compartment S
= 57 x 32 x 10.32
= 18823.68 cm
3 Volume of water flowed from S to T in 1 minute
= 18823.68 ÷ 105
≈ 179.3 cm
3 Answer(s): (a) 27.68 cm; (b) 179.3 cm
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