A tank holds some water up to a height of 82 cm. When 4 identical wooden cubes are put into the tank, the water level rises by 28 cm. One wooden cube is then removed from the tank, replaced by one iron cube. The water level increases to 136 cm.
- Find the ratio of the volume of 1 wooden cube to 1 iron cube.
- If the base area of the tank is 122 cm², find the difference in the volume between the iron cube and the wooden cube. Express your answer in cm³.
(a)
4 wooden cubes → water level rises by 28 cm
Height of water per wooden cube
= 28 ÷ 4
= 7 cm
Height of water after one wooden cube is removed
= 82 + 28 - 7
= 103 cm
Height of water increased with 1 iron cube
= 136 - 103
= 33 cm
Ratio of the change in height of the wooden cube to the iron cube
= 7 : 33
(b)
Difference between the height of the iron cube and the wooden cube
= 33 - 7
= 26 cm
Difference between volume of the iron cube and the wooden cube
= 26 x 122
= 3172 cm
3 Answer(s): (a) 7 : 33; (b) 3172 cm
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