This figure is not drawn to scale. A rectangular glass tank 90 cm by 59 cm by 45 cm has 2 compartments, F and G, with a water height of 39 cm in F and 12 cm in G. A hole in the slider caused water to leak from F to G. 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 1¹₄ 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 F to G in 1 minute? Express your answer to 1 decimal place in cm³.

(a)
Volume of water in Compartment F
= 28 x 39 x 59
= 64428 cm³ 

Length of Compartment G
= 90 - 28
= 62 cm

Volume of the water in Compartment G
= 62 x 59 x 12
= 43896 cm³ 

Total volume of water
= 64428 + 43896
= 108324 cm³ 

Base area of the glass tank
= 90 x 59
= 5310 cm² 

Height of water
= 108324 ÷ 5310
= 20.4 cm

(b)
1¹₄ h = 75 min

Drop in the height of Compartment F
= 39 - 20.4
= 18.6 cm

Drop in the volume of Compartment F
= 59 x 28 x 18.6
= 30727.2 cm³ 

Volume of water flowed from F to G in 1 minute
= 30727.2 ÷ 75
≈ 409.7 cm³

Answer(s): (a) 20.4 cm; (b) 409.7 cm³