This figure is not drawn to scale. A rectangular glass container 75 cm by 53 cm by 47 cm has 2 compartments, L and M, with a water height of 37 cm in L and 16 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 container now?
2. It took 1¹₂ 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 53
= 62752 cm³ 

Length of Compartment M
= 75 - 32
= 43 cm

Volume of the water in Compartment M
= 43 x 53 x 16
= 36464 cm³ 

Total volume of water
= 62752 + 36464
= 99216 cm³ 

Base area of the glass container
= 75 x 53
= 3975 cm² 

Height of water
= 99216 ÷ 3975
= 24.96 cm

(b)
1¹₂ h = 90 min

Drop in the height of Compartment L
= 37 - 24.96
= 12.04 cm

Drop in the volume of Compartment L
= 53 x 32 x 12.04
= 20419.84 cm³ 

Volume of water flowed from L to M in 1 minute
= 20419.84 ÷ 90
≈ 226.9 cm³

Answer(s): (a) 24.96 cm; (b) 226.9 cm³