Question

The portion of the parabola y² =4a x bounded by the line x-e revolves about the axis. Find the

volume generated. Show also that it is equal to half the volume of the cylinder whose base-radius is the extreme ordinate and height the abscissa. .​

Answer 1

Answer:

Let O be the vertex,S be the focus and LL

′

be the latus rectum of araboal.

The equation of latus rectum is x=a

Also , we know that parabola is symmetric about x−axis

∴ Required Area=2(areaOSL)

=2∫

0

a

y.dx

=2∫

0

a

2

a

x

.dx

=4

a

∫

0

a

x

.dx

=4

a

⎣

⎢

⎢

⎡

2

3

x

2

3

⎦

⎥

⎥

⎤

0

a

=

3

8

a

a

2

3

=

3

8a

2

sq.units