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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.

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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.3dw:1357858021843:dw

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.3Do 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.3dw: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.3dw:1357858535828:dw Subtract the right volume from the left. Got it?

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.3dw:1357858823945:dw It is like subtracting this areas.

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.3\(V=\pi\int_{1}^1(\sqrt{1x^2}+2)^2dx\pi\int_{1}^1(\sqrt{1x^2}+2)^2dx\)

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.3If 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.3if 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.3But 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.3Have 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.3It 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.3Yes. 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.3Yes. The volume of the doughnut.dw:1357861006645:dw
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