A tank holds some water up to a height of 91 cm. When 7 identical plastic cubes are put into the tank, the water level rises by 35 cm. One plastic cube is then removed from the tank, replaced by one iron cube. The water level increases to 139 cm.

1. Find the ratio of the volume of 1 plastic cube to 1 iron cube.
2. If the base area of the tank is 152 cm², find the difference in the volume between the iron cube and the plastic cube.  Express your answer in cm³.

(a)
7 plastic cubes → water level rises by 35 cm

Height of water per plastic cube
= 35 ÷ 7
= 5 cm

Height of water after one plastic cube is removed
= 91 + 35 - 5
= 121 cm

Height of water increased with 1 iron cube
= 139 - 121
= 18 cm

Ratio of the change in height of the plastic cube to the iron cube
= 5 : 18 

(b)

Difference between the height of the iron cube and the plastic cube
= 18 - 5
= 13 cm

Difference between volume of the iron cube and the plastic cube
= 13 x 152
= 1976 cm³ 

Answer(s): (a) 5 : 18; (b) 1976 cm³