Volume by Integration

Derivation of Formula for Volume of the Sphere by Integration

For detailed information about sphere, see the Solid Geometry entry, The Sphere.
 

The formula for the volume of the sphere is given by

Example 2 | Volumes of Solids of Revolution

Example 2
Find the volume generated when the area in Example 1 will revolve about the y-axis.
 

Example 1 | Volumes of Solids of Revolution

Example 1
Find the volume of the solid generated when the area bounded by the curve y2 = x, the x-axis and the line x = 2 is revolved about the x-axis.
 

Volumes of Solids of Revolution | Applications of Integration

Solids of Revolution by Integration

The solid generated by rotating a plane area about an axis in its plane is called a solid of revolution. The volume of a solid of revolution may be found by the following procedures:
 

 
 
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