A tank holds some water up to a height of 103 cm. When 2 identical wooden balls are put into the tank, the water level rises by 16 cm. One wooden ball is then removed from the tank, replaced by one metallic ball. The water level increases to 138 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 189 cm², find the difference in the volume between the metallic ball and the wooden ball.  Express your answer in cm³.

(a)
2 wooden balls → water level rises by 16 cm

Height of water per wooden ball
= 16 ÷ 2
= 8 cm

Height of water after one wooden ball is removed
= 103 + 16 - 8
= 111 cm

Height of water increased with 1 metallic ball
= 138 - 111
= 27 cm

Ratio of the change in height of the wooden ball to the metallic ball
= 8 : 27 

(b)

Difference between the height of the metallic ball and the wooden ball
= 27 - 8
= 19 cm

Difference between volume of the metallic ball and the wooden ball
= 19 x 189
= 3591 cm³ 

Answer(s): (a) 8 : 27; (b) 3591 cm³