Question

A square is drawn inside a square. Find the area of the square as a function of the radius of the circle.

Answer 1

The diameter of the circle is 2*Radius

area of square= diameter^2= 4 * R^2

Answer 2

so that is the answer

Answer 3

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

Answer 4

which one is the correct answer

Answer 5

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

Answer 6

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