Asked by kim

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

Answers

Answered by bobpursley
The diameter of the circle is 2*Radius

area of square= diameter^2= 4 * R^2
Answered by kim
so that is the answer
Answered by 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
Answered by kim
which one is the correct answer
Answered by Damon
Draw a graph. Start at x = 0 and work your way up to x = pi/6
Answered by 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
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