This figure is not drawn to scale. A rectangular glass tank 70 cm by 57 cm by 46 cm has 2 compartments, Q and R, with a water height of 31 cm in Q and 17 cm in R. A hole in the slider caused water to leak from Q to R. 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 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 Q to R in 1 minute? Express your answer to 1 decimal place in cm³.

(a)
Volume of water in Compartment Q
= 25 x 31 x 57
= 44175 cm³ 

Length of Compartment R
= 70 - 25
= 45 cm

Volume of the water in Compartment R
= 45 x 57 x 17
= 43605 cm³ 

Total volume of water
= 44175 + 43605
= 87780 cm³ 

Base area of the glass tank
= 70 x 57
= 3990 cm² 

Height of water
= 87780 ÷ 3990
= 22 cm

(b)
1¹₂ h = 90 min

Drop in the height of Compartment Q
= 31 - 22
= 9 cm

Drop in the volume of Compartment Q
= 57 x 25 x 9
= 12825 cm³ 

Volume of water flowed from Q to R in 1 minute
= 12825 ÷ 90
≈ 142.5 cm³

Answer(s): (a) 22 cm; (b) 142.5 cm³