This figure is not drawn to scale. A rectangular glass container 72 cm by 60 cm by 50 cm has 2 compartments, X and Y, with a water height of 33 cm in X and 20 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 container now?
2. 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 X to Y in 1 minute? Express your answer to 1 decimal place in cm³.

(a)
Volume of water in Compartment X
= 36 x 33 x 60
= 71280 cm³ 

Length of Compartment Y
= 72 - 36
= 36 cm

Volume of the water in Compartment Y
= 36 x 60 x 20
= 43200 cm³ 

Total volume of water
= 71280 + 43200
= 114480 cm³ 

Base area of the glass container
= 72 x 60
= 4320 cm² 

Height of water
= 114480 ÷ 4320
= 26.5 cm

(b)
1³₄ h = 105 min

Drop in the height of Compartment X
= 33 - 26.5
= 6.5 cm

Drop in the volume of Compartment X
= 60 x 36 x 6.5
= 14040 cm³ 

Volume of water flowed from X to Y in 1 minute
= 14040 ÷ 105
≈ 133.7 cm³

Answer(s): (a) 26.5 cm; (b) 133.7 cm³