A container holds some water up to a height of 74 cm. When 2 identical plastic balls are put into the container, the water level rises by 20 cm. One plastic ball is then removed from the tank, replaced by one metallic ball. The water level increases to 137 cm.

1. Find the ratio of the volume of 1 plastic ball to 1 metallic ball.
2. If the base area of the container is 181 cm², find the difference in the volume between the metallic ball and the plastic ball.  Express your answer in cm³.

(a)
2 plastic balls → water level rises by 20 cm

Height of water per plastic ball
= 20 ÷ 2
= 10 cm

Height of water after one plastic ball is removed
= 74 + 20 - 10
= 84 cm

Height of water increased with 1 metallic ball
= 137 - 84
= 53 cm

Ratio of the change in height of the plastic ball to the metallic ball
= 10 : 53 

(b)

Difference between the height of the metallic ball and the plastic ball
= 53 - 10
= 43 cm

Difference between volume of the metallic ball and the plastic ball
= 43 x 181
= 7783 cm³ 

Answer(s): (a) 10 : 53; (b) 7783 cm³