A tank holds some water up to a height of 87 cm. When 6 identical wooden balls are put into the tank, the water level rises by 30 cm. One wooden ball is then removed from the tank, replaced by one metallic ball. The water level increases to 130 cm.

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

(a)
6 wooden balls → water level rises by 30 cm

Height of water per wooden ball
= 30 ÷ 6
= 5 cm

Height of water after one wooden ball is removed
= 87 + 30 - 5
= 112 cm

Height of water increased with 1 metallic ball
= 130 - 112
= 18 cm

Ratio of the change in height of the wooden ball to the metallic ball
= 5 : 18 

(b)

Difference between the height of the metallic ball and the wooden ball
= 18 - 5
= 13 cm

Difference between volume of the metallic ball and the wooden ball
= 13 x 85
= 1105 cm³ 

Answer(s): (a) 5 : 18; (b) 1105 cm³