Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

The question is this

Please tell me if what I did is correct or if there's any faster alternatives.

I set $x$ and $y$ axes on the center of the circle with radius $r$, therefore this can be seen as an area described by $x^2+y^2=r$ revolving around $x=-R-r$

$dV$ can be written as $$dV = 2\pi(R+x)\cdot 2y \cdot dx =2\pi(R+x)\cdot 2 \sqrt{r-x^2} \cdot dx$$

$V$ is then
$$ \int_R^{R+2r} 4\pi(R+x)\sqrt{r-x^2} dx $$

Is this correct?

share|improve this question
1  
You should have $r^2$ under the square root. Your integration range is not correct, it's a range for $x$ and thus should be $[-r,r]$. Anyway, isn't an integral a bit of overkill for this? A bit of thinking can solve the problem with elementary geometrical formulas. –  Raskolnikov Feb 9 '11 at 17:36
1  
@Raskolnikov: it is probably a homework question, and since the question explicitly asked for setting up an integral, I think the OP may not get credit if he doesn't do it that way. –  Willie Wong Feb 9 '11 at 17:41
    
Duplicate question: math.stackexchange.com/questions/11735/… –  TonyK Feb 9 '11 at 18:07
    
@Raskolnikov: So if use the shell method, the integral should be $$ \int_{-r}^{r} 4\pi(R+x)\sqrt{r^2-x^2} dx $$ ? –  xiamx Feb 10 '11 at 15:40
    
Yes, I think that should be it. –  Raskolnikov Feb 10 '11 at 17:08
show 2 more comments

1 Answer

up vote 1 down vote accepted

hint: in addition to what Raskolnikov said, it may be simpler to consider the washer method instead of the shell method for setting up your integral. (That is, integrate in $y$ and consider the area of annuli of the constant $y$ slices.)

share|improve this answer
    
I tried the washer method and found $$ V= 8\pi R \int_0^{r} \sqrt{r^2-y^2} dy $$ –  xiamx Feb 10 '11 at 15:37
    
And you probably know how to evaluate that particular integral. Hint: it is the area under a certain curve, what is the curve? –  Willie Wong Feb 10 '11 at 16:59
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.