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Home Applications of the Integral Infinite Sum Theorem Problems  
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Problems
1 The base of a solid is the triangle in the x, yplane with vertices at (0, 0), (0, 1), and (1, 0). The cross sections perpendicular to the xaxis are squares with one side on the base. Find the volume of the solid. 2 The base of a solid is the region in the x, yplane bounded by the parabola y = x^{2 }and the line y = 1. The cross sections perpendicular to the xaxis are squares with one side on the base. Find the volume of the solid. 3 Find the volume of the solid in Problem 1 if the cross sections are equilateral triangles with one side on the base. 4 Find the volume of the solid in Problem 2 if the cross sections are equilateral triangles with one side on the base. 5 Find the volume of the solid in Problem 1 if the cross sections are semicircles with diameter on the base. 6 Find the volume of the solid in Problem 2 if the cross sections are semicircles with diameter on the base. 7 Find the volume of a wedge cut from a circular cylinder of radius r by two planes whose line of intersection passes through the axis of the cylinder, if the wedge has thickness c at its thickest point. 8 Find the volume of the smaller wedge cut from a circular cylinder of radius r by two planes whose line of intersection is a chord at distance b from the axis of the cylinder, if the greatest thickness is c.


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