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Home Applications of the Integral Volumes of Solids of Revolution Solids of Revolution  
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Solids of Revolution
Integrals are used in this section to find the volume of a solid of revolution. A solid of revolution is generated by taking a region in the first quadrant of the plane and rotating it in space about the x or yaxis (Figure 6.2.1). Figure 6.2.1 Solids of Revolution We shall work with the region under a curve and the region between two curves. We use one method for rotating about the axis of the independent variable and another for rotating about the axis of the dependent variable. For areas our starting point was the formula area = base × height for the area of a rectangle. For volumes of a solid of revolution our starting point is the usual formula for the volume of a right circular cylinder (Figure 6.2.2). Figure 6.2.2 DEFINITION The volume of a right circular cylinder with height h and base of radius r is V = πr^{2}h.


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