A container holds some water up to a height of 84 cm. When 4 identical wooden balls are put into the container, the water level rises by 28 cm. One wooden ball is then removed from the tank, replaced by one iron ball. The water level increases to 132 cm.

1. Find the ratio of the volume of 1 wooden ball to 1 iron ball.
2. If the base area of the container is 287 cm², find the difference in the volume between the iron ball and the wooden ball.  Express your answer in cm³.

(a)
4 wooden balls → water level rises by 28 cm

Height of water per wooden ball
= 28 ÷ 4
= 7 cm

Height of water after one wooden ball is removed
= 84 + 28 - 7
= 105 cm

Height of water increased with 1 iron ball
= 132 - 105
= 27 cm

Ratio of the change in height of the wooden ball to the iron ball
= 7 : 27 

(b)

Difference between the height of the iron ball and the wooden ball
= 27 - 7
= 20 cm

Difference between volume of the iron ball and the wooden ball
= 20 x 287
= 5740 cm³ 

Answer(s): (a) 7 : 27; (b) 5740 cm³