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anonymous
 4 years ago
Can anyone prove the volume of an ellipse?
anonymous
 4 years ago
Can anyone prove the volume of an ellipse?

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Do you mean find an area or actually prove the formula?

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.2yeah i can zoom in. so basically they want you to use calculus to derive the formula for volume of a 3d ellipse

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.2ok, start with equation of ellipse: \[\frac{x^{2}}{b^{2}} +\frac{y^{2}}{a^{2}} = 1\] dw:1327556444323:dw then integrate from b to b, of A(x) which is the area of each circular crosssection where the radius is y: solve the ellipse equation for y \[y = \sqrt{a^{2}  \frac{a^{2}}{b^{2}}x^{2}} = \frac{a}{b}\sqrt{b^{2}x^{2}}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Thanks for ur help :D That was awesome and very clear

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0wait how did u get that equation

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0like from the first to the second

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0but do i have to integrate it?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0or is this the end result?

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.2sorry i skipped some simplifying steps.. no you still have to integrate \[V = \pi \int\limits_{b}^{b}y^{2} dx\] plug that equation in for y

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0huh i doubt i will be able to integrate that on my own

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.2ok \[y^{2} = \frac{a^{2}}{b^{2}}(b^{2}x^{2})\] factor out the constants \[V = \frac{a^{2} \pi}{b^{2}}\int\limits_{b}^{b} (b^{2} x^{2}) dx\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1327557477105:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1327557564379:dw

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.2not quite, you skipped a step first evaluate from b to b by plugging them in for x

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.2we don't want x in our answer

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1327557858057:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1327557996710:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0This shld be the answer :D

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.2looks good :) don;t forget about the pi

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0oh yes thanks for ur help and patience

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.2this is the same way of finding volume of sphere as well just make a =b
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