This figure is not drawn to scale. A rectangular glass tank 75 cm by 58 cm by 48 cm has 2 compartments, T and U, with a water height of 30 cm in T and 20 cm in U. A hole in the slider caused water to leak from T to U. 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 T to U in 1 minute? Express your answer to 1 decimal place in cm³.

(a)
Volume of water in Compartment T
= 21 x 30 x 58
= 36540 cm³ 

Length of Compartment U
= 75 - 21
= 54 cm

Volume of the water in Compartment U
= 54 x 58 x 20
= 62640 cm³ 

Total volume of water
= 36540 + 62640
= 99180 cm³ 

Base area of the glass tank
= 75 x 58
= 4350 cm² 

Height of water
= 99180 ÷ 4350
= 22.8 cm

(b)
1¹₄ h = 75 min

Drop in the height of Compartment T
= 30 - 22.8
= 7.2 cm

Drop in the volume of Compartment T
= 58 x 21 x 7.2
= 8769.6 cm³ 

Volume of water flowed from T to U in 1 minute
= 8769.6 ÷ 75
≈ 116.9 cm³

Answer(s): (a) 22.8 cm; (b) 116.9 cm³