This figure is not drawn to scale. A rectangular glass tank 90 cm by 53 cm by 42 cm has 2 compartments, N and P, with a water height of 30 cm in N and 12 cm in P. A hole in the slider caused water to leak from N to P. 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 N to P in 1 minute? Express your answer to 1 decimal place in cm³.

(a)
Volume of water in Compartment N
= 34 x 30 x 53
= 54060 cm³ 

Length of Compartment P
= 90 - 34
= 56 cm

Volume of the water in Compartment P
= 56 x 53 x 12
= 35616 cm³ 

Total volume of water
= 54060 + 35616
= 89676 cm³ 

Base area of the glass tank
= 90 x 53
= 4770 cm² 

Height of water
= 89676 ÷ 4770
= 18.8 cm

(b)
1¹₄ h = 75 min

Drop in the height of Compartment N
= 30 - 18.8
= 11.2 cm

Drop in the volume of Compartment N
= 53 x 34 x 11.2
= 20182.4 cm³ 

Volume of water flowed from N to P in 1 minute
= 20182.4 ÷ 75
≈ 269.1 cm³

Answer(s): (a) 18.8 cm; (b) 269.1 cm³