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Volume of solid obtained by revolving the area of the ellipse $\large\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}$=$1$ about major and minor axes are in the ratio

\[\begin{array}{1 1}(1)b^{2}:a^{2}&(2)a^{2}:b^{2}\\(3)a:b&(4)b:a\end{array}\]

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The volume of the solid obtained y revolving the area of the ellipse $\large\frac{x^2}{a^2} +\frac{y^2}{b^2}$$=1$ about axis $=\large\frac{4 \pi }{3}$$ \; a^2 \;cu. units$
The volume of the solid obtained y revolving the area of the ellipse $\large\frac{x^2}{a^2} +\frac{y^2}{b^2}$$=1$ about minor axis $=\large\frac{4 \pi}{3}$$ a^2\;cu. units $
Ratio of the volume $= \large\frac{\Large\frac{4 \pi}{3} ab^2}{\Large\frac{4 \pi}{3} a^2b} $$=\large\frac{b}{a}$
Ratio is $b:a$
Hence 4 is the correct answer.
answered May 21, 2014 by meena.p
 

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