# 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 y^{2} = 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: