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A cylindrical can containing pieces of f...

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 `cm^2`, and the height of the can is 10 cm. If 110 `cm^3` 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?

A

`7.5 cm^3`

B

`185 cm^3`

C

`640 cm^3`

D

`750 cm^3`

Text Solution

Verified by Experts

The correct Answer is:
C
The total volume of the cylindrical can is found by multiplying the area of the base of the can, 75 cm2, by the height of the can, 10 cm, which yields 750 `cm^(3)`. If the syrup needed to fill the can has a volume of 110 `cm^(3)`, then the remaining volume for the pieces of fruit is 750 – 110 = 640 `cm^(3)`.
Choice A is incorrect because if the fruit had a volume of 7.5 `cm^(3)`, there would be 750 – 7.5 = 742.5 `cm^(3)` of syrup needed to fill the can to the top. Choice B is incorrect because if the fruit had a volume of 185 `cm^(3)`, there would be 750 – 185 = 565 `cm^(3)` 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.
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