A container holds some water up to a height of 92 cm. When 3 identical plastic balls are put into the container, the water level rises by 21 cm. One plastic ball is then removed from the tank, replaced by one metallic ball. The water level increases to 131 cm.
- Find the ratio of the volume of 1 plastic ball to 1 metallic ball.
- If the base area of the container is 128 cm², find the difference in the volume between the metallic ball and the plastic ball. Express your answer in cm³.
(a)
3 plastic balls → water level rises by 21 cm
Height of water per plastic ball
= 21 ÷ 3
= 7 cm
Height of water after one plastic ball is removed
= 92 + 21 - 7
= 106 cm
Height of water increased with 1 metallic ball
= 131 - 106
= 25 cm
Ratio of the change in height of the plastic ball to the metallic ball
= 7 : 25
(b)
Difference between the height of the metallic ball and the plastic ball
= 25 - 7
= 18 cm
Difference between volume of the metallic ball and the plastic ball
= 18 x 128
= 2304 cm
3 Answer(s): (a) 7 : 25; (b) 2304 cm
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