A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
Moyo30
 2 years ago
Find the volume of the torus (doughnut) formed by rotating the circle x2 + (y − 2)2 = 1 about the xaxis.
Moyo30
 2 years ago
Find the volume of the torus (doughnut) formed by rotating the circle x2 + (y − 2)2 = 1 about the xaxis.

This Question is Closed

Moyo30
 2 years ago
Best ResponseYou've already chosen the best response.0Hint: \[\int\limits_{1}^{1}\sqrt{1x ^{2}}=\frac{ \pi }{ 2 }\]

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1357858021843:dw

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.2Do you know the formula for the volume of solid rotating \(y=f(x)\) about \(x\)axis?

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1357858353355:dw

Moyo30
 2 years ago
Best ResponseYou've already chosen the best response.0\[\pi \int\limits_{a}^{b}f(x)dx\]

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1357858535828:dw Subtract the right volume from the left. Got it?

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1357858823945:dw It is like subtracting this areas.

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.2\(V=\pi\int_{1}^1(\sqrt{1x^2}+2)^2dx\pi\int_{1}^1(\sqrt{1x^2}+2)^2dx\)

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.2If you don't get it now just sit and think about it very thoroughly.

Moyo30
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1357858979556:dw the graph of x^2+(y2)^2=1 is something like that how do we get to the penultimate drawing

Moyo30
 2 years ago
Best ResponseYou've already chosen the best response.0i kinda get it you reflect a portion of the circle in the x axis and find the region bounded by the two arcsdw:1357859345394:dw

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.2if you try to write y depending on x, you will get 2 functions: \(y=\sqrt{1x^2}+2\) and \(y=\sqrt{1x^2}+2\). Now think what will be if you rotate them about xaxes. And then use your imagination to unterstand how to get the needed volume. Really the plot is:dw:1357859397346:dw

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.2But if you are lazy and dishonest student you can just use the formulas I've written above.

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.2Have you understood something?

Moyo30
 2 years ago
Best ResponseYou've already chosen the best response.0yes it is basically a volume but it complicated by the fact that the function that we get after making y the subject of the formula is composed of two equations so we add the two. right?

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.2It is very hard to tell if you got something or not. I don't know your level of knowledge. Tell me honestly: can you find the area between \(y=x^2\) and \(y=1x^2\)?

Moyo30
 2 years ago
Best ResponseYou've already chosen the best response.0subtract x^2 from 1x^2 and integrate

Moyo30
 2 years ago
Best ResponseYou've already chosen the best response.0juss realised my prob no squaring

Moyo30
 2 years ago
Best ResponseYou've already chosen the best response.0integrate, limits the intersection of the lines

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.2Yes. The similar situation is here. But now we have a volume to subtract. Hope, you got something, if not  very bad.

Moyo30
 2 years ago
Best ResponseYou've already chosen the best response.0so basically in this prob they ask us to find the volume rather than the area

Moyo30
 2 years ago
Best ResponseYou've already chosen the best response.0can you pls draw the resultant volume if it is not too diff

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.2Yes. The volume of the doughnut.dw:1357861006645:dw
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.