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Moyo30
Group Title
Find the volume of the torus (doughnut) formed by rotating the circle x2 + (y − 2)2 = 1 about the xaxis.
 one year ago
 one year ago
Moyo30 Group Title
Find the volume of the torus (doughnut) formed by rotating the circle x2 + (y − 2)2 = 1 about the xaxis.
 one year ago
 one year ago

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

klimenkov Group TitleBest ResponseYou've already chosen the best response.2
dw:1357858021843:dw
 one year ago

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

klimenkov Group TitleBest ResponseYou've already chosen the best response.2
dw:1357858353355:dw
 one year ago

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

klimenkov Group TitleBest ResponseYou've already chosen the best response.2
You forgot 2.
 one year ago

klimenkov Group TitleBest ResponseYou've already chosen the best response.2
dw:1357858535828:dw Subtract the right volume from the left. Got it?
 one year ago

Moyo30 Group TitleBest ResponseYou've already chosen the best response.0
y subtracting?
 one year ago

klimenkov Group TitleBest ResponseYou've already chosen the best response.2
dw:1357858823945:dw It is like subtracting this areas.
 one year ago

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

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

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

Moyo30 Group TitleBest ResponseYou've already chosen the best response.0
i 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
 one year ago

klimenkov Group TitleBest ResponseYou've already chosen the best response.2
if 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
 one year ago

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

klimenkov Group TitleBest ResponseYou've already chosen the best response.2
Have you understood something?
 one year ago

Moyo30 Group TitleBest ResponseYou've already chosen the best response.0
yes 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?
 one year ago

klimenkov Group TitleBest ResponseYou've already chosen the best response.2
It 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 \(y=1x^2\)?
 one year ago

Moyo30 Group TitleBest ResponseYou've already chosen the best response.0
subtract x^2 from 1x^2 and integrate
 one year ago

klimenkov Group TitleBest ResponseYou've already chosen the best response.2
Why square?
 one year ago

Moyo30 Group TitleBest ResponseYou've already chosen the best response.0
juss realised my prob no squaring
 one year ago

Moyo30 Group TitleBest ResponseYou've already chosen the best response.0
integrate, limits the intersection of the lines
 one year ago

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

Moyo30 Group TitleBest ResponseYou've already chosen the best response.0
so basically in this prob they ask us to find the volume rather than the area
 one year ago

Moyo30 Group TitleBest ResponseYou've already chosen the best response.0
can you pls draw the resultant volume if it is not too diff
 one year ago

klimenkov Group TitleBest ResponseYou've already chosen the best response.2
Yes. The volume of the doughnut.dw:1357861006645:dw
 one year ago

Moyo30 Group TitleBest ResponseYou've already chosen the best response.0
thx for your help
 one year ago
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