A tank holds some water up to a height of 75 cm. When 2 identical wooden balls are put into the tank, the water level rises by 46 cm. One wooden ball is then removed from the tank, replaced by one iron ball. The water level increases to 136 cm.

1. Find the ratio of the volume of 1 wooden ball to 1 iron ball.
2. If the base area of the tank is 79 cm², find the difference in the volume between the iron ball and the wooden ball.  Express your answer in cm³.

(a)
2 wooden balls → water level rises by 46 cm

Height of water per wooden ball
= 46 ÷ 2
= 23 cm

Height of water after one wooden ball is removed
= 75 + 46 - 23
= 98 cm

Height of water increased with 1 iron ball
= 136 - 98
= 38 cm

Ratio of the change in height of the wooden ball to the iron ball
= 23 : 38 

(b)

Difference between the height of the iron ball and the wooden ball
= 38 - 23
= 15 cm

Difference between volume of the iron ball and the wooden ball
= 15 x 79
= 1185 cm³ 

Answer(s): (a) 23 : 38; (b) 1185 cm³