A tank holds some water up to a height of 82 cm. When 3 identical plastic cubes are put into the tank, the water level rises by 39 cm. One plastic cube is then removed from the tank, replaced by one metallic cube. The water level increases to 135 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 143 cm², find the difference in the volume between the metallic cube and the plastic cube.  Express your answer in cm³.

(a)
3 plastic cubes → water level rises by 39 cm

Height of water per plastic cube
= 39 ÷ 3
= 13 cm

Height of water after one plastic cube is removed
= 82 + 39 - 13
= 108 cm

Height of water increased with 1 metallic cube
= 135 - 108
= 27 cm

Ratio of the change in height of the plastic cube to the metallic cube
= 13 : 27 

(b)

Difference between the height of the metallic cube and the plastic cube
= 27 - 13
= 14 cm

Difference between volume of the metallic cube and the plastic cube
= 14 x 143
= 2002 cm³ 

Answer(s): (a) 13 : 27; (b) 2002 cm³