SOLUTION: How many circular cookies measuring 2 inches in radius can be cut from a circle of dough measuring 6 inches in radius, assuming that dough between the cookies is not reused?

Question 833336: How many circular cookies measuring 2 inches in radius can be cut from a circle of dough measuring 6 inches in radius, assuming that dough between the cookies is not reused?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!

cookies
The least unused space between cookies and the edge of the dough circle will be achieved when the cookies are against the edge of the dough circle.
The least unused space between cookies will be achieved when the cookie centers are forming an equilateral triangle. Three of a cookie wedges will be inside that triangle. The area of that of a circle of radius is , while the triangle, with sides measuring will have a height of and an area of .
The fraction of that area covered by the circle wedges is
= approx. 0.91 (91%).
If you place circles with radius so that the centers form a square, the side of that square will be and the area of that square will be , while the 4 quarter circle wedges covering that square will have a total area of , amounting to
= approx. 0.79 (79%) of the square area.
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