A tank holds some water up to a height of 106 cm. When 6 identical rubber cubes are put into the tank, the water level rises by 12 cm. One rubber cube is then removed from the tank, replaced by one metallic cube. The water level increases to 137 cm.

1. Find the ratio of the volume of 1 rubber cube to 1 metallic cube.
2. If the base area of the tank is 144 cm², find the difference in the volume between the metallic cube and the rubber cube.  Express your answer in cm³.

(a)
6 rubber cubes → water level rises by 12 cm

Height of water per rubber cube
= 12 ÷ 6
= 2 cm

Height of water after one rubber cube is removed
= 106 + 12 - 2
= 116 cm

Height of water increased with 1 metallic cube
= 137 - 116
= 21 cm

Ratio of the change in height of the rubber cube to the metallic cube
= 2 : 21 

(b)

Difference between the height of the metallic cube and the rubber cube
= 21 - 2
= 19 cm

Difference between volume of the metallic cube and the rubber cube
= 19 x 144
= 2736 cm³ 

Answer(s): (a) 2 : 21; (b) 2736 cm³