A container holds some water up to a height of 76 cm. When 2 identical wooden cubes are put into the container, the water level rises by 22 cm. One wooden cube is then removed from the tank, replaced by one iron cube. The water level increases to 135 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 224 cm², find the difference in the volume between the iron cube and the wooden cube.  Express your answer in cm³.

(a)
2 wooden cubes → water level rises by 22 cm

Height of water per wooden cube
= 22 ÷ 2
= 11 cm

Height of water after one wooden cube is removed
= 76 + 22 - 11
= 87 cm

Height of water increased with 1 iron cube
= 135 - 87
= 48 cm

Ratio of the change in height of the wooden cube to the iron cube
= 11 : 48 

(b)

Difference between the height of the iron cube and the wooden cube
= 48 - 11
= 37 cm

Difference between volume of the iron cube and the wooden cube
= 37 x 224
= 8288 cm³ 

Answer(s): (a) 11 : 48; (b) 8288 cm³