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Geometry and Trigonometry Difficulty: Medium

A cylindrical can containing pieces of fruit is filled to the top with syrup before being sealed. The base of the can has an area of $75 centimeters squared$ , and the height of the can is 10 cm. If $110 centimeters cubed$ of syrup is needed to fill the can to the top, which of the following is closest to the total volume of the pieces of fruit in the can?

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Explanation

Choice C is correct. The total volume of the cylindrical can is found by multiplying the area of the base of the can, $75 square centimeters$ , by the height of the can, 10 cm, which yields $750 cubic centimeters$ . If the syrup needed to fill the can has a volume of $110 cubic centimeters$ , then the remaining volume for the pieces of
fruit is $750 minus 110, equals 640 cubic centimeters$ .

Choice A is incorrect because if the fruit had a volume of $7 point 5 cubic centimeters$ , there would be $750 minus 7 point 5, equals 742 point 5 cubic centimeters$ of syrup needed to fill the can to the top. Choice B is incorrect because if the fruit had a volume of $185 cubic centimeters$ , there would be $750 minus 185, equals 565 cubic centimeters$ of syrup needed to fill the can to the top. Choice D is incorrect because it is the total volume of the can, not just of the pieces of fruit.