Posted by kim on .
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,
The diameter of the circle is 2*Radius
area of square= diameter^2= 4 * R^2 
pre calc 
kim,
so that is the answer

pre calc 
Damon,
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,
which one is the correct answer

pre calc 
Damon,
Draw a graph. Start at x = 0 and work your way up to x = pi/6

pre calc 
Damon,
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