A tank holds some water up to a height of 76 cm. When 7 identical rubber cubes are put into the tank, the water level rises by 35 cm. One rubber cube is then removed from the tank, replaced by one iron cube. The water level increases to 132 cm.
- Find the ratio of the volume of 1 rubber cube to 1 iron cube.
- If the base area of the tank is 275 cm², find the difference in the volume between the iron cube and the rubber cube. Express your answer in cm³.
(a)
7 rubber cubes → water level rises by 35 cm
Height of water per rubber cube
= 35 ÷ 7
= 5 cm
Height of water after one rubber cube is removed
= 76 + 35 - 5
= 106 cm
Height of water increased with 1 iron cube
= 132 - 106
= 26 cm
Ratio of the change in height of the rubber cube to the iron cube
= 5 : 26
(b)
Difference between the height of the iron cube and the rubber cube
= 26 - 5
= 21 cm
Difference between volume of the iron cube and the rubber cube
= 21 x 275
= 5775 cm
3 Answer(s): (a) 5 : 26; (b) 5775 cm
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