SOLUTION: A circle is drawn in a square whose side has a length of 40. Find the area of the shaded region in terms of pie.
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Question 219100: A circle is drawn in a square whose side has a length of 40. Find the area of the shaded region in terms of pie.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Be delighted to help you if you would be so very kind as to share a description of "the shaded area." We can't see your picture. However, I will help you this much:
Presuming that the circle is inscribed in the square, which is to say that all four sides of the square are tangent to the circle, then you can say this:
If the side of the square is 40, then the area of the entire square is 
. 40 is also a diameter of the circle, hence the radius of the circle is then 20. Hence the area of the circle is 
. The sum of the areas of the four little corner pieces that are part of the square but not of the circle is then the area of the square minus the area of the circle, i.e., 
. If you only need one of those little pieces, then the area is one-fourth the area of all four of them, or 
Oh, and one more thing: "pie" is a dessert item, usually with a flaky crust, and frequently with a fruit filling. "pi" is the Greek letter representing the ratio of a circle's circumference to its diameter. Therefore, I am assuming that you need to express your answer to this question in terms of "pi" rather than "pie."
John
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