A tank holds some water up to a height of 116 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 iron ball. The water level increases to 135 cm.
- Find the ratio of the volume of 1 rubber ball to 1 iron ball.
- If the base area of the tank is 299 cm², find the difference in the volume between the iron 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
= 116 + 10 - 2
= 124 cm
Height of water increased with 1 iron ball
= 135 - 124
= 11 cm
Ratio of the change in height of the rubber ball to the iron ball
= 2 : 11
(b)
Difference between the height of the iron ball and the rubber ball
= 11 - 2
= 9 cm
Difference between volume of the iron ball and the rubber ball
= 9 x 299
= 2691 cm
3 Answer(s): (a) 2 : 11; (b) 2691 cm
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