A square piece of cardboard of sides ten inches is taken and four equal square pieces are removed at the corners. The sides are then turned up to form an open box. Then the maximum volume such a box can have is

Each side of a given polygon is parallel to either the X or the Y axis. A corner of such a polygon is said to be convex if the internal angle is 90^o or concave if the internal angle is 270^o. If the number of convex corners in such a polygon is 25, the number of concave corners must be

A circle is inscribed in a given square and another circle is circumscribed about the square. What is the ratio of the area of the inscribed circle to that of the circumscribed circle ?