Question

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

• A. $b^2:a^2$
• B. $a^2:b^2$
• C. $a:b$
• D. $b:a$

Answer 1

The correct option is D $b:a$

Given ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Thus major axis is $a$ and minor axis is $b$

The volume of the solid obtained by revolving the area of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ about major axis is $\frac{4\pi }{3}a{b}^{2}cu.units$

The volume of the solid obtained by revolving the area of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ about minor axis is $\frac{4\pi }{3}{a}^{2}bcu.units$

Ratio of the volume $=\frac{\frac{4}{3}\pi a{b}^2}{\frac{4}{3}\pi a^{2}b}=\frac{b}{a}$

Hence the ratio is $b:a$