A tank holds some water up to a height of 117 cm. When 5 identical rubber balls are put into the tank, the water level rises by 10 cm. One rubber ball is then removed from the tank, replaced by one metallic ball. The water level increases to 138 cm.

1. Find the ratio of the volume of 1 rubber ball to 1 metallic ball.
2. If the base area of the tank is 251 cm², find the difference in the volume between the metallic ball and the rubber ball.  Express your answer in cm³.

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

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

Height of water after one rubber ball is removed
= 117 + 10 - 2
= 125 cm

Height of water increased with 1 metallic ball
= 138 - 125
= 13 cm

Ratio of the change in height of the rubber ball to the metallic ball
= 2 : 13 

(b)

Difference between the height of the metallic ball and the rubber ball
= 13 - 2
= 11 cm

Difference between volume of the metallic ball and the rubber ball
= 11 x 251
= 2761 cm³ 

Answer(s): (a) 2 : 13; (b) 2761 cm³