A cubical container of edge 20 cm was filled to the brim with oil. The oil was then poured into a rectangular tank that already had some oil in it. The ratio of the volume of oil in the rectangular tank to the volume of the cubical container became 5 : 4. Find the volume of oil that was in the rectangular tank at first. Volume of oil in the rectangular tank at first: _____ cm³
Question
A cubical container of edge 20 cm was filled to the brim with oil. The oil was then poured into a rectangular tank that already had some oil in it. The ratio of the volume of oil in the rectangular tank to the volume of the cubical container became 5 : 4. Find the volume of oil that was in the rectangular tank at first. Volume of oil in the rectangular tank at first: _____ cm³
Solution
To solve this problem, we need to follow these steps:
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First, we need to find the volume of the cubical container. The volume of a cube is given by the formula V = a³, where a is the length of an edge. So, the volume of the cubical container is 20 cm * 20 cm * 20 cm = 8000 cm³.
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The problem states that after the oil from the cubical container was poured into the rectangular tank, the ratio of the volume of oil in the rectangular tank to the volume of the cubical container became 5 : 4. This means that the volume of the rectangular tank is 5/4 times the volume of the cubical container, or 1.25 * 8000 cm³ = 10000 cm³.
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To find the volume of oil that was in the rectangular tank at first, we subtract the volume of the cubical container from the total volume of the rectangular tank after the oil was added. So, the volume of oil in the rectangular tank at first was 10000 cm³ - 8000 cm³ = 2000 cm³.
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