A tank holds some water up to a height of 107 cm. When 5 identical wooden cubes are put into the tank, the water level rises by 15 cm. One wooden cube is then removed from the tank, replaced by one metallic cube. The water level increases to 130 cm.

1. Find the ratio of the volume of 1 wooden cube to 1 metallic cube.
2. If the base area of the tank is 293 cm², find the difference in the volume between the metallic cube and the wooden cube.  Express your answer in cm³.

(a)
5 wooden cubes → water level rises by 15 cm

Height of water per wooden cube
= 15 ÷ 5
= 3 cm

Height of water after one wooden cube is removed
= 107 + 15 - 3
= 119 cm

Height of water increased with 1 metallic cube
= 130 - 119
= 11 cm

Ratio of the change in height of the wooden cube to the metallic cube
= 3 : 11 

(b)

Difference between the height of the metallic cube and the wooden cube
= 11 - 3
= 8 cm

Difference between volume of the metallic cube and the wooden cube
= 8 x 293
= 2344 cm³ 

Answer(s): (a) 3 : 11; (b) 2344 cm³