This figure is not drawn to scale. A rectangular glass tank 84 cm by 52 cm by 42 cm has 2 compartments, X and Y, with a water height of 40 cm in X and 19 cm in Y. A hole in the slider caused water to leak from X to Y. It was found that the water level in both compartments became the same after some time.

1. What is the height of water in the tank now?
2. 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 X to Y in 1 minute? Express your answer to 1 decimal place in cm³.

(a)
Volume of water in Compartment X
= 31 x 40 x 52
= 64480 cm³ 

Length of Compartment Y
= 84 - 31
= 53 cm

Volume of the water in Compartment Y
= 53 x 52 x 19
= 52364 cm³ 

Total volume of water
= 64480 + 52364
= 116844 cm³ 

Base area of the glass tank
= 84 x 52
= 4368 cm² 

Height of water
= 116844 ÷ 4368
= 26.75 cm

(b)
1¹₅ h = 72 min

Drop in the height of Compartment X
= 40 - 26.75
= 13.25 cm

Drop in the volume of Compartment X
= 52 x 31 x 13.25
= 21359 cm³ 

Volume of water flowed from X to Y in 1 minute
= 21359 ÷ 72
≈ 296.7 cm³

Answer(s): (a) 26.75 cm; (b) 296.7 cm³