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Those Barrels of Oil
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So what was the answer to the question about the barrels of oil A certain barrel, which is a right circular cylinder, is filled to capacity with 100 gallons of oil The first barrel is poured into a second barrel, also a right circular cylinder, which is empty The second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel If all of the oil in the first barrel is poured into the second barrel, how much empty capacity, in gallons, is left in the second barrel A There is no empty capacity B 100 gallons C 300 gallons D 700 gallons E 800 gallons The answer is D We don t know what the actual dimensions of the first barrel are, but we know that the volume of a cylinder = r2h (r = radius and h = height), and in the case of the first barrel, r 2h = 100 gallons We don t know the exact dimensions of the second barrel either, but we know that its height is twice that of the first barrel, so 2h, and its diameter is twice that of the first barrel, and since the diameter of a circle is double the radius, it follows that the radius of the second barrel must be twice that of the first barrel as well, so 2r The volume of the second barrel, therefore, is = (2r)2(2h) = 8 r2h = 8 ( r2h) Therefore, the second barrel has a volume eight times that of the first barrel, so 8 100 gallons = 800 gallons If the 100 gallons in the first barrel are poured into the second barrel, then the remaining empty capacity of the second barrel is 800 gallons minus the 100 gallons, which equals 700 gallons
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