A container holds some water up to a height of 76 cm. When 4 identical plastic balls are put into the container, the water level rises by 36 cm. One plastic ball is then removed from the tank, replaced by one iron ball. The water level increases to 135 cm.

1. Find the ratio of the volume of 1 plastic ball to 1 iron ball.
2. If the base area of the container is 162 cm², find the difference in the volume between the iron ball and the plastic ball.  Express your answer in cm³.

(a)
4 plastic balls → water level rises by 36 cm

Height of water per plastic ball
= 36 ÷ 4
= 9 cm

Height of water after one plastic ball is removed
= 76 + 36 - 9
= 103 cm

Height of water increased with 1 iron ball
= 135 - 103
= 32 cm

Ratio of the change in height of the plastic ball to the iron ball
= 9 : 32 

(b)

Difference between the height of the iron ball and the plastic ball
= 32 - 9
= 23 cm

Difference between volume of the iron ball and the plastic ball
= 23 x 162
= 3726 cm³ 

Answer(s): (a) 9 : 32; (b) 3726 cm³