Show proofs of Archimedes theorem that the area of a circle = pir^2

a rectangle can be drawn in the first quadrant bounded by the curve y= 8- x^3 , the x- axis and the y- axis. Determine the dimension length and width of the largest rectangle that can be drawn

B is the name and the center point of one circle and C is the name and the center point of another circle and both circles B and C touch each other externally and both circles are the same size too. Also, "A" is a point on the circumference of circle C. From this is drawn segment BA which has a length of (24)3^(1/2) and is tangent at point A on circle C. What are the radii of circles B and C?  I've just looked at a unit circle's coordinates and figured that radius=[(24)3^(1/2)]x[1/(2)3^(1/2)]=12. So, radius for both circle B and circle C is 12.

SOLVE FOR NUMBER 8    8. Suppose the parabola y = 9 - x^2  is shifted three units to the right. Find theslope of the line y = mx which divides the area of the shifted parabola in half.