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So I have this square and theres a circle inside of it. The circle of radius $r$ is inscribed in the square. So how do I find the area of the square in terms of $r$? I know that area of a circle is $\pi r^2$, but they wouldn't give me the area of the parts of the square the circle doesn't cover. any help?

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1 Answer 1

Hint: Think about the relationship between the radius of the circle, the diameter of the circle, and the side length of the square.

$\hskip1.5in$ enter image description here

Do you know the area of a square given its side length?

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ok, if im getting somewhere, the radius of the circle is half the length of one side of the square, and the area of the square is s^2, so, in terms of r, would it be 2r^2? –  Ronnie.j Sep 20 '11 at 1:43
    
@Ronnie: Close, but not quite. The side length $s$ of the square is equal to $2r$, but $$\text{area of square} = s^2=(2r)^2=(2\times r)\times (2\times r)=4\times r\times r = 4r^2$$ not $2r^2$. –  Zev Chonoles Sep 20 '11 at 1:45
    
yea i meant (2r)^2 sorry lol –  Ronnie.j Sep 20 '11 at 1:48
    
@Ronnie: Ah, ok :) If my answer has been helpful, you can upvote it (by clicking on the little "up arrow" on the upper left of my answer, above the number) or accept it (by clicking the green check mark a little below that), if you would like. –  Zev Chonoles Sep 20 '11 at 1:50
    
done and done. Theres another question i need help with. I have 3000 feet of fencing, and im suppose to find the area of the rectangle with x as the length. I did A=x*(3000-2x). Now it asks to find for what value of x is the area largest, and im stuck as to what to do? –  Ronnie.j Sep 20 '11 at 1:57

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