Question

Use Shell Method to find Volume, rotated about x-axis.

Answer 1

I know that:

\[V=\int\limits_{a}^{b} 2\pi (shell radius) (shell height) dx\]

Answer 2

So far, I have:

\[V=2\pi \int\limits_{0}^{6} (radius) (height) dx\]

Answer 3

What is the radius? And is the height \[\sqrt{6}\] ?

Answer 4

if you are making a bowl like thing with this shell, wouldnt the radius depend on where you are taking your measurement? and then the height would be 6 i think because that is the point where the radius of the open circle is the largest?

Answer 5

i am not 100 percent sure. I'll take a look through my old notes and try and remember this

Answer 6

try :

\[\large V=2\pi \int\limits_{0}^{\color{red}{\sqrt{6}}} (radius) (height) \color{red}{dy}\]

Answer 7

radius of shell = \(\large y\)
height of shell = \(\large x = y^2\)

Answer 8

is the radius y?

Answer 9

yes! that

Answer 10

\[\large V=2\pi \int\limits_{0}^{\color{red}{\sqrt{6}}} (y) (y^2) \color{red}{dy}\]

Answer 11

yes :)

Answer 12

ugh... volume is 2pi r^2 *height? or not r^2?

Answer 13

no r^2 in this formula

Answer 14

spin it around x axis