A tank holds some water up to a height of 108 cm. When 2 identical rubber cubes are put into the tank, the water level rises by 20 cm. One rubber cube is then removed from the tank, replaced by one iron cube. The water level increases to 137 cm.

1. Find the ratio of the volume of 1 rubber cube to 1 iron cube.
2. If the base area of the tank is 133 cm², find the difference in the volume between the iron cube and the rubber cube.  Express your answer in cm³.

(a)
2 rubber cubes → water level rises by 20 cm

Height of water per rubber cube
= 20 ÷ 2
= 10 cm

Height of water after one rubber cube is removed
= 108 + 20 - 10
= 118 cm

Height of water increased with 1 iron cube
= 137 - 118
= 19 cm

Ratio of the change in height of the rubber cube to the iron cube
= 10 : 19 

(b)

Difference between the height of the iron cube and the rubber cube
= 19 - 10
= 9 cm

Difference between volume of the iron cube and the rubber cube
= 9 x 133
= 1197 cm³ 

Answer(s): (a) 10 : 19; (b) 1197 cm³