This figure is not drawn to scale. A rectangular glass tank 88 cm by 53 cm by 48 cm has 2 compartments, S and T, with a water height of 36 cm in S and 14 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 tank 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
= 18 x 36 x 53
= 34344 cm
3 Length of Compartment T
= 88 - 18
= 70 cm
Volume of the water in Compartment T
= 70 x 53 x 14
= 51940 cm
3 Total volume of water
= 34344 + 51940
= 86284 cm
3 Base area of the glass tank
= 88 x 53
= 4664 cm
2 Height of water
= 86284 ÷ 4664
= 18.5 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment S
= 36 - 18.5
= 17.5 cm
Drop in the volume of Compartment S
= 53 x 18 x 17.5
= 16695 cm
3 Volume of water flowed from S to T in 1 minute
= 16695 ÷ 75
≈ 222.6 cm
3 Answer(s): (a) 18.5 cm; (b) 222.6 cm
3