This figure is not drawn to scale. A rectangular glass container 90 cm by 50 cm by 47 cm has 2 compartments, U and V, with a water height of 30 cm in U and 12 cm in V. A hole in the slider caused water to leak from U to V. 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 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 U to V in 1 minute? Express your answer to 1 decimal place in cm³.

(a)
Volume of water in Compartment U
= 32 x 30 x 50
= 48000 cm³ 

Length of Compartment V
= 90 - 32
= 58 cm

Volume of the water in Compartment V
= 58 x 50 x 12
= 34800 cm³ 

Total volume of water
= 48000 + 34800
= 82800 cm³ 

Base area of the glass container
= 90 x 50
= 4500 cm² 

Height of water
= 82800 ÷ 4500
= 18.4 cm

(b)
1¹₅ h = 72 min

Drop in the height of Compartment U
= 30 - 18.4
= 11.6 cm

Drop in the volume of Compartment U
= 50 x 32 x 11.6
= 18560 cm³ 

Volume of water flowed from U to V in 1 minute
= 18560 ÷ 72
≈ 257.8 cm³

Answer(s): (a) 18.4 cm; (b) 257.8 cm³