Method
A volume(rotated around the xaxis)is calculated by first considering a particular value of a function, y_{1}, up from a value of x at x_{1} . The line x_{1}y_{1} may be considered as the 'radius' of the solid at that particular value of x.
If you were to square the yvalue and multiply it by pi, then a crosssectional area would be created.
Making a solid of revolution is simply the method of summing all the crosssectional areas along the xaxis between two values of x.
(compare: area of a cylinder = crosssectional area x length)
The method for solids rotated around the yaxis is similar.
Rotation around the xaxis
The volume V_{x}of a curve y=f(x) rotated around the xaxis between the values of x of a and b, is given by:
Example
What is the volume V of the cone swept out by the line y=2x rotated about the xaxis between x=0 and x=5?
Rotation around the yaxis
The volume V_{y}of a curve y=f(x) rotated around the xaxis between the values of y of c and d, is given by:
Example
What is the volume V of the 'frustrum'(cone with smaller coneshape removed) produced when the line y=2x/3 is rotated around the yaxis, when the centres of the upper and lower areas of the frustrum are at 0,7 and 0,3

