A container holds some water up to a height of 97 cm. When 2 identical rubber balls are put into the container, the water level rises by 10 cm. One rubber ball is then removed from the tank, replaced by one iron ball. The water level increases to 138 cm.

1. Find the ratio of the volume of 1 rubber ball to 1 iron ball.
2. If the base area of the container is 159 cm², find the difference in the volume between the iron ball and the rubber ball.  Express your answer in cm³.

(a)
2 rubber balls → water level rises by 10 cm

Height of water per rubber ball
= 10 ÷ 2
= 5 cm

Height of water after one rubber ball is removed
= 97 + 10 - 5
= 102 cm

Height of water increased with 1 iron ball
= 138 - 102
= 36 cm

Ratio of the change in height of the rubber ball to the iron ball
= 5 : 36 

(b)

Difference between the height of the iron ball and the rubber ball
= 36 - 5
= 31 cm

Difference between volume of the iron ball and the rubber ball
= 31 x 159
= 4929 cm³ 

Answer(s): (a) 5 : 36; (b) 4929 cm³