This figure is not drawn to scale. A rectangular glass container 76 cm by 55 cm by 49 cm has 2 compartments, P and Q, with a water height of 32 cm in P and 13 cm in Q. A hole in the slider caused water to leak from P to Q. 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 P to Q in 1 minute? Express your answer to 1 decimal place in cm³.

(a)
Volume of water in Compartment P
= 25 x 32 x 55
= 44000 cm³ 

Length of Compartment Q
= 76 - 25
= 51 cm

Volume of the water in Compartment Q
= 51 x 55 x 13
= 36465 cm³ 

Total volume of water
= 44000 + 36465
= 80465 cm³ 

Base area of the glass container
= 76 x 55
= 4180 cm² 

Height of water
= 80465 ÷ 4180
= 19.25 cm

(b)
1³₄ h = 105 min

Drop in the height of Compartment P
= 32 - 19.25
= 12.75 cm

Drop in the volume of Compartment P
= 55 x 25 x 12.75
= 17531.25 cm³ 

Volume of water flowed from P to Q in 1 minute
= 17531.25 ÷ 105
≈ 167 cm³

Answer(s): (a) 19.25 cm; (b) 167 cm³