The figure is not drawn to scale. It shows a tank made from two connected cubical containers, Cube H and Cube J. The tank is filled with some water. Cube H is ²₃ filled with 13122 mℓ of water while Cube J is completely filled with water. The height of the water level in Cube H is 5 cm higher than that in Cube J. Water is then drained from the tank and the height of the new water level is 6 cm. What is the volume of the water drained in mℓ?
²₃ of the volume of Cube H = 13122 mℓ

Volume of Cube H
= 13122 ÷ ²₃
= 13122 x ³₂
= 19683 mℓ

Length of Cube H
= ³√19683
= 27 cm 

Height of water in Cube H at first
= ²₃ x 27
= 18 cm

Height of Cube J
= 18 - 5
= 13 cm

Height decrease in water in Cube H after draining
= 18 - 6
= 12 cm

Height decrease in water in Cube H after draining
= 13 - 6
= 7 cm

Volume of water drained in Cube H
= 27 x 27 x 12
= 8748 mℓ

Volume of water drained in Cube J
= 13 x 13 x 7
= 1183 mℓ

Total volume of water drained
= 8748 + 1183
= 9931 mℓ

Answer(s): 9931 mℓ