This figure is not drawn to scale. A rectangular glass tank 80 cm by 53 cm by 41 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 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
= 12 x 38 x 53
= 24168 cm
3 Length of Compartment T
= 80 - 12
= 68 cm
Volume of the water in Compartment T
= 68 x 53 x 20
= 72080 cm
3 Total volume of water
= 24168 + 72080
= 96248 cm
3 Base area of the glass tank
= 80 x 53
= 4240 cm
2 Height of water
= 96248 ÷ 4240
= 22.7 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment S
= 38 - 22.7
= 15.3 cm
Drop in the volume of Compartment S
= 53 x 12 x 15.3
= 9730.8 cm
3 Volume of water flowed from S to T in 1 minute
= 9730.8 ÷ 75
≈ 129.7 cm
3 Answer(s): (a) 22.7 cm; (b) 129.7 cm
3