# What is the surface area of the solid created by revolving #f(t) = ( t^3-t, t^3-t, t in [2,3]# around the x-axis?

##### 1 Answer

not including the area of the end caps, S =

#### Explanation:

if you look at the parameterisation,

and the interval specified corresponds in Cartesian to

maybe there is a typo here as bothering with the calculus seems overkill but we can proceed anyways.

starting with the simple idea of arc length, viz that

the elemental surface area of revolution is therefore

so Surface Area is

and as the params are the same,

so we have

This is what you would get from the formula for the surface are of a truncated cone

**NB this does not include the area of the end caps.**