A sculptor has a cylindrical piece of clay. How can the sculptor slice the clay to make a slice that is the shape of a rectangle?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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The sculptor can slice the cylindrical piece of clay to create rectangles only if the cylinder is a rectangular one. Or put differently, when the cylinder is placed such that it is standing on its base, the base and the top are parallel to each other and each of them is perpendicular to the vertical axis.

To create rectangular slices the sculptor has to cut very thin slices, and the cuts have to be made perpendicular to base. The thinner the slices are, the closer they will be to attaining the shape of perfect rectangles.

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senseigreen | Middle School Teacher | (Level 1) eNoter

Posted on

A chin scratcher almost as classic as square peg vs. round hole (Hint-Hint). The solver of this should not be shaken by the circles on the ends, but rather embrace the symmetry of them.

Taking the third dimensional view, you can simply slice along the center (cut the pie in half) the length of the cylinder and you will have TWO, 2 dimensional rectangles of the greatest area. ANY radial slices will expose smaller rectangles which are half that area.

The slices from any section of the circle, made parallel to each other will be of increasing area until they meet at the center point of the circle. LASTLY, if you inscibed a square within the radius of the circle, you will re-create a rectangular prism in its place.

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