A tank holds some water up to a height of 108 cm. When 2 identical plastic cubes are put into the tank, the water level rises by 22 cm. One plastic cube is then removed from the tank, replaced by one metallic cube. The water level increases to 136 cm.

1. Find the ratio of the volume of 1 plastic cube to 1 metallic cube.
2. If the base area of the tank is 115 cm², find the difference in the volume between the metallic cube and the plastic cube.  Express your answer in cm³.

(a)
2 plastic cubes → water level rises by 22 cm

Height of water per plastic cube
= 22 ÷ 2
= 11 cm

Height of water after one plastic cube is removed
= 108 + 22 - 11
= 119 cm

Height of water increased with 1 metallic cube
= 136 - 119
= 17 cm

Ratio of the change in height of the plastic cube to the metallic cube
= 11 : 17 

(b)

Difference between the height of the metallic cube and the plastic cube
= 17 - 11
= 6 cm

Difference between volume of the metallic cube and the plastic cube
= 6 x 115
= 690 cm³ 

Answer(s): (a) 11 : 17; (b) 690 cm³