This figure is not drawn to scale. A rectangular glass tank 90 cm by 52 cm by 47 cm has 2 compartments, H and J, with a water height of 33 cm in H and 15 cm in J. A hole in the slider caused water to leak from H to J. 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 H to J in 1 minute? Express your answer to 1 decimal place in cm³.

(a)
Volume of water in Compartment H
= 20 x 33 x 52
= 34320 cm³ 

Length of Compartment J
= 90 - 20
= 70 cm

Volume of the water in Compartment J
= 70 x 52 x 15
= 54600 cm³ 

Total volume of water
= 34320 + 54600
= 88920 cm³ 

Base area of the glass tank
= 90 x 52
= 4680 cm² 

Height of water
= 88920 ÷ 4680
= 19 cm

(b)
1¹₂ h = 90 min

Drop in the height of Compartment H
= 33 - 19
= 14 cm

Drop in the volume of Compartment H
= 52 x 20 x 14
= 14560 cm³ 

Volume of water flowed from H to J in 1 minute
= 14560 ÷ 90
≈ 161.8 cm³

Answer(s): (a) 19 cm; (b) 161.8 cm³