This figure is not drawn to scale. A rectangular glass tank 75 cm by 56 cm by 50 cm has 2 compartments, L and M, with a water height of 37 cm in L and 10 cm in M. A hole in the slider caused water to leak from L to M. 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 L to M in 1 minute? Express your answer to 1 decimal place in cm³.

(a)
Volume of water in Compartment L
= 32 x 37 x 56
= 66304 cm³ 

Length of Compartment M
= 75 - 32
= 43 cm

Volume of the water in Compartment M
= 43 x 56 x 10
= 24080 cm³ 

Total volume of water
= 66304 + 24080
= 90384 cm³ 

Base area of the glass tank
= 75 x 56
= 4200 cm² 

Height of water
= 90384 ÷ 4200
= 21.52 cm

(b)
1¹₅ h = 72 min

Drop in the height of Compartment L
= 37 - 21.52
= 15.48 cm

Drop in the volume of Compartment L
= 56 x 32 x 15.48
= 27740.16 cm³ 

Volume of water flowed from L to M in 1 minute
= 27740.16 ÷ 72
≈ 385.3 cm³

Answer(s): (a) 21.52 cm; (b) 385.3 cm³