A container holds some water up to a height of 72 cm. When 7 identical wooden cubes are put into the container, the water level rises by 42 cm. One wooden 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 wooden cube to 1 iron cube.
2. If the base area of the container is 65 cm², find the difference in the volume between the iron cube and the wooden cube.  Express your answer in cm³.

(a)
7 wooden cubes → water level rises by 42 cm

Height of water per wooden cube
= 42 ÷ 7
= 6 cm

Height of water after one wooden cube is removed
= 72 + 42 - 6
= 108 cm

Height of water increased with 1 iron cube
= 137 - 108
= 29 cm

Ratio of the change in height of the wooden cube to the iron cube
= 6 : 29 

(b)

Difference between the height of the iron cube and the wooden cube
= 29 - 6
= 23 cm

Difference between volume of the iron cube and the wooden cube
= 23 x 65
= 1495 cm³ 

Answer(s): (a) 6 : 29; (b) 1495 cm³