Math C Question on 'Volumes of Revolution'

Ok so I have the two coordinates (0,3) and (2,7)

The line that runs through them is y=2x+3

How do I find the volume created by rotating the line around the x axis..

In other words, I will be using *volumes of revolution*.

However, I have only bee taught on this how to just find the volume of a straight line only using one coordinate. Would it work the same or would I need to use both coordinates? Would the limits be from 0 to 7? and then intergrating 4x^2+12x+9 and multiplying it by pie?

Many thanks to those who reply

Re: Math C Question on 'Volumes of Revolution'

Quote:

Originally Posted by

**BryannaAllan** Ok so I have the two coordinates (0,3) and (2,7)

The line that runs through them is y=2x+3

How do I find the volume created by rotating the line around the x axis..

In other words, I will be using *volumes of revolution*.

If you want to use calculus then

$\displaystyle \int_0^2 {2\pi {r^2}dx}$ where $\displaystyle r=(2x+3)$.

However, simple algebra will work. It is the difference of the volumes of two cones.