A container holds some water up to a height of 92 cm. When 2 identical wooden cubes are put into the container, the water level rises by 10 cm. One wooden cube is then removed from the tank, replaced by one metallic cube. The water level increases to 134 cm.

1. Find the ratio of the volume of 1 wooden cube to 1 metallic cube.
2. If the base area of the container is 85 cm², find the difference in the volume between the metallic cube and the wooden cube.  Express your answer in cm³.

(a)
2 wooden cubes → water level rises by 10 cm

Height of water per wooden cube
= 10 ÷ 2
= 5 cm

Height of water after one wooden cube is removed
= 92 + 10 - 5
= 97 cm

Height of water increased with 1 metallic cube
= 134 - 97
= 37 cm

Ratio of the change in height of the wooden cube to the metallic cube
= 5 : 37 

(b)

Difference between the height of the metallic cube and the wooden cube
= 37 - 5
= 32 cm

Difference between volume of the metallic cube and the wooden cube
= 32 x 85
= 2720 cm³ 

Answer(s): (a) 5 : 37; (b) 2720 cm³