This figure is not drawn to scale. A rectangular glass tank 72 cm by 58 cm by 44 cm has 2 compartments, S and T, with a water height of 31 cm in S and 13 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 115 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
= 29 x 31 x 58
= 52142 cm
3 Length of Compartment T
= 72 - 29
= 43 cm
Volume of the water in Compartment T
= 43 x 58 x 13
= 32422 cm
3 Total volume of water
= 52142 + 32422
= 84564 cm
3 Base area of the glass tank
= 72 x 58
= 4176 cm
2 Height of water
= 84564 ÷ 4176
= 20.25 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment S
= 31 - 20.25
= 10.75 cm
Drop in the volume of Compartment S
= 58 x 29 x 10.75
= 18081.5 cm
3 Volume of water flowed from S to T in 1 minute
= 18081.5 ÷ 72
≈ 251.1 cm
3 Answer(s): (a) 20.25 cm; (b) 251.1 cm
3