Math CentralQuandaries & Queries


Question from Brix, a student:

A cylinder fits perfectly in a box. 76 cubic inches of oil is poured into the space between the cylinder and the box, filling the space halfway. If the box is 3ft wide, how tall is the cylinder in inches?

Hi Brix.

To solve this, you need to first think two dimensionally, then three.

The question doesn't say so, but I think you are to assume that thecylinder is upright in the box, rather than lying on its side.

The box bottom therefore, is square, to "perfectly" contain the cylinder, whose bottom is a circle with the same diameter as the box's side, 3 feet.

3 feet is 12 inches, so the box bottom is 12 x 12, which makes 144 square inches. The area that the oil will go is everyone over this square EXCEPT the circle in the middle. The radius of the circle is 6 inches, so you can use that to find the area of the circle, then subtract that from the total 144 square inches and you will know the area the oil will cover.

Then you would just multiply by the height of the oil to find the volume. But since you are told the volume of oil (76 cubic inches) by the area and you will get the height in inches of the oil.

Remember the height of the oil is half the height of the cylinder, so you need to double it to answer the question.

Good luck!
Stephen La Rocque.

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