Posted by kim on Thursday, January 14, 2010 at 5:38pm.
A square is drawn inside a square. Find the area of the square as a function of the radius of the circle.

pre calc  bobpursley, Thursday, January 14, 2010 at 5:40pm
The diameter of the circle is 2*Radius
area of square= diameter^2= 4 * R^2

pre calc  kim, Thursday, January 14, 2010 at 5:42pm
so that is the answer

pre calc  Damon, Thursday, January 14, 2010 at 5:47pm
No, the diameter of the circle is the diagonal of the square
Side of square = D/sqrt2
Area of square = D^2/2
but D = 2 R
so
area of square = 4 R^2/2 = 2 R^2

pre calc  kim, Thursday, January 14, 2010 at 5:50pm
which one is the correct answer

pre calc  Damon, Thursday, January 14, 2010 at 5:52pm
Draw a graph. Start at x = 0 and work your way up to x = pi/6

pre calc  Damon, Thursday, January 14, 2010 at 5:57pm
Oh, sorry, worong question. Draw your square inside the circle and you will see that the diagonal of the square is the diameter of the circle.
The diagonal of the square divides the square into two 45,45,90 triangles
The hypotenuse of a 45,45,90 triangle id the side times sqrt 2
s^2+s^2 = diagonal^2
2 s^2 = diagonal^2
s = (1/sqrt2) diagonal
so
diagonal = side * sqrt 2 = diameter
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