A container holds some water up to a height of 90 cm. When 2 identical plastic cubes are put into the container, the water level rises by 14 cm. One plastic cube is then removed from the tank, replaced by one metallic cube. The water level increases to 133 cm.

1. Find the ratio of the volume of 1 plastic cube to 1 metallic cube.
2. If the base area of the container is 159 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 14 cm

Height of water per plastic cube
= 14 ÷ 2
= 7 cm

Height of water after one plastic cube is removed
= 90 + 14 - 7
= 97 cm

Height of water increased with 1 metallic cube
= 133 - 97
= 36 cm

Ratio of the change in height of the plastic cube to the metallic cube
= 7 : 36 

(b)

Difference between the height of the metallic cube and the plastic cube
= 36 - 7
= 29 cm

Difference between volume of the metallic cube and the plastic cube
= 29 x 159
= 4611 cm³ 

Answer(s): (a) 7 : 36; (b) 4611 cm³