SOLUTION: a circle is inside a square and line from left to right across with a on left side and b on right side--question is if line ab (diameter) is 82cm--what is left not covered by the
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Question 438554: a circle is inside a square and line from left to right across with a on left side and b on right side--question is if line ab (diameter) is 82cm--what is left not covered by the circle Answer by solver91311(24713) (Show Source):
I'll solve the problem in general and then you can apply the solution to your specific case.
If a circle is inscribed in a square, that is the circle is tangent to all 4 sides of the square, then the diameter of the circle and the side of the square are congruent.
Let represent the diameter of the circle.
1. Since the diameter of the circle is congruent with the side of the square, the area of the square is represented by .
2. Since the radius of a circle is half of the diameter, the radius of this circle is . And the area of the circle is then ( times the radius squared)
3. The desired area is the area of the square minus the area of the circle, so:
A little algebra:
And a little calculator work:
Hence, roughly 21.5% of the square remains uncovered. All you need now is the area of your given square and multiply by 0.215]
John
My calculator said it, I believe it, that settles it
