Question

g

Answer 1

Could you explain your set up (while I work on what I am thinking about and we will be able to compare) ?

Answer 2

yes:

I'm only looking at a quarter of the centered at origin circle.

Answer 3

(the upper quarter right one)

Answer 4

I'm using the shell method.

So, circumference of shell is 2pi(R-x)

Answer 5

height= sqroot(1-x^2)

Answer 6

width=dx

Answer 7

do the integral

Answer 8

from 0 to 1

Answer 9

multiply by 4 to get total volume

Answer 10

I don't think you can split it into four parts and use only one quadrant.
The piece on the second quadrant is actually larger because it is further away than the one on the interior, right?


Instead, try splitting it into the top half and the bottom half. You can still integrate from -1 to 1 and R+x or R-x.

Answer 11

Then you just take the top half integral and multiply by 2.

Answer 12

OHHHHHHHHHH i didnt see this.

Answer 13

Sudden revelation!

Answer 14

I will try it. I'll be back in a couple of seconds.

Answer 15

Yep, that seems correct to me. :)

Answer 16

oh that sense of satisfaction :)

Answer 17

Yea, that threw me for a loop as well because I was thinking "well of course these four quadrants are the same size, it has to work?" and then I drew the picture and thought about how it worked out there. :p