Given a solid with base defined by the ordinate set of a continuous function on the interval . The cross sections take perpendicular to are in the shape of squares. Find the function if the volume of the solid is

The volume of the solid is equal to the integral,

since the cross sections are in the shape of squares and the length of the base is . So the cross sectional area at each point from 1 to is , and then the volume is obtained by integrating these areas over . Setting this equal to the given formula for the volume,