This figure is not drawn to scale. A rectangular glass tank 78 cm by 52 cm by 50 cm has 2 compartments, P and Q, with a water height of 38 cm in P and 14 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 tank now?
2. 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 P to Q in 1 minute? Express your answer to 1 decimal place in cm³.

(a)
Volume of water in Compartment P
= 39 x 38 x 52
= 77064 cm³ 

Length of Compartment Q
= 78 - 39
= 39 cm

Volume of the water in Compartment Q
= 39 x 52 x 14
= 28392 cm³ 

Total volume of water
= 77064 + 28392
= 105456 cm³ 

Base area of the glass tank
= 78 x 52
= 4056 cm² 

Height of water
= 105456 ÷ 4056
= 26 cm

(b)
1¹₄ h = 75 min

Drop in the height of Compartment P
= 38 - 26
= 12 cm

Drop in the volume of Compartment P
= 52 x 39 x 12
= 24336 cm³ 

Volume of water flowed from P to Q in 1 minute
= 24336 ÷ 75
≈ 324.5 cm³

Answer(s): (a) 26 cm; (b) 324.5 cm³