This figure is not drawn to scale. A rectangular glass container 74 cm by 58 cm by 50 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 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
= 37 x 33 x 58
= 70818 cm
3 Length of Compartment T
= 74 - 37
= 37 cm
Volume of the water in Compartment T
= 37 x 58 x 16
= 34336 cm
3 Total volume of water
= 70818 + 34336
= 105154 cm
3 Base area of the glass container
= 74 x 58
= 4292 cm
2 Height of water
= 105154 ÷ 4292
= 24.5 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment S
= 33 - 24.5
= 8.5 cm
Drop in the volume of Compartment S
= 58 x 37 x 8.5
= 18241 cm
3 Volume of water flowed from S to T in 1 minute
= 18241 ÷ 105
≈ 173.7 cm
3 Answer(s): (a) 24.5 cm; (b) 173.7 cm
3