Volume of Solid of Revolution Question

[reybob]

Homework Statement

y= -(x/6) + b, find the volume as this solid is rotated 360 degrees around the Y axis

Homework Equations

If I were given the interval at which I needed to find the volume and/or the value of B I could easily do this using the formula:

[pi] Integrate: (R(y))² dx

The Attempt at a Solution

What I am trying to ascertain is whether or not this problem is even doable. I don't know if my professor intentionally left out the interval and b value and wants us to do it algebraically but I can't move ahead as most of the questions are based off this one. Please help!

 

[hunt_mat]

The general formula for this is given by:
$$V=\pi\int_{a}^{b}y^{2}(x)dx$$

 

[reybob]

is it possible to do this question without being given the bounds or knowing where the line sits? Because there is no y intercept and I'm not too sure how you would find the volume without enough information to get the area of the original shape

 

[tiny-tim]

welcome to pf!

hi reybob! welcome to pf!

y= -(x/6) + b, find the volume as this solid is rotated 360 degrees around the Y axis
…
What I am trying to ascertain is whether or not this problem is even doable.

no, without limits it makes no sense

 

[LCKurtz]

Homework Statement

y= -(x/6) + b, find the volume as this solid is rotated 360 degrees around the Y axis

Homework Equations

If I were given the interval at which I needed to find the volume and/or the value of B I could easily do this using the formula:

[pi] Integrate: (R(y))² dx

Of course, you mean dy.

You could make up your own x or y limits of c and d and leave your answer as a function of c, d, and b. Better might be to ask the prof if he forgot to include limits.

 

[reybob]

Yeah I think I'm going to have to do that. Thank you so much for all this help, this forum rocks!