This figure is not drawn to scale. A rectangular glass container 85 cm by 54 cm by 48 cm has 2 compartments, S and T, with a water height of 36 cm in S and 19 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
= 18 x 36 x 54
= 34992 cm
3 Length of Compartment T
= 85 - 18
= 67 cm
Volume of the water in Compartment T
= 67 x 54 x 19
= 68742 cm
3 Total volume of water
= 34992 + 68742
= 103734 cm
3 Base area of the glass container
= 85 x 54
= 4590 cm
2 Height of water
= 103734 ÷ 4590
= 22.6 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment S
= 36 - 22.6
= 13.4 cm
Drop in the volume of Compartment S
= 54 x 18 x 13.4
= 13024.8 cm
3 Volume of water flowed from S to T in 1 minute
= 13024.8 ÷ 105
≈ 124 cm
3 Answer(s): (a) 22.6 cm; (b) 124 cm
3