Question

8.
Find the volume generated by revolving the ellipse
x2 y2
+ =1 about x-axis.
Ans: 4871
16 9
of the solid curve cardioid
be
fone
ran​

Answer 1

Answer:

b/a

Step-by-step explanation:

Take a small disc at a length of x from the centre of thickness dx. Then the volume of solid obtained by rotation will be ∫  

−a

a

​  

(Area)dx

Area of disc =πr  

2

 

r can be calculated from the equation of ellipse as

a  

2

 

x  

2

 

​  

+  

b  

2

 

r  

2

 

​  

=1

⇒r  

2

=b  

2

(1−  

a  

2

 

x  

2

 

​  

)=  

a  

2

 

b  

2

 

​  

(a  

2

−x  

2

)

∴Volume  

major axis

​  

=∫  

−a

a

​  

π  

a  

2

 

b  

2

 

​  

(a  

2

−x  

2

)dx=[πb  

2

x−  

3a  

2

 

πb  

2

x  

3

 

​  

]  

−a

a

​  

=  

3

4

​  

πab  

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Answer 2

Answer:

sorry I can't understand your question please asked again.