Question

Find the volume of the solid generated by revolving the region bounded by (x-h)^2 +y^2 = r^2 , (h>r) about the y-axis? Any takers? Thanks!

Answer 1

this is calc III?

Answer 2

first draw the circle (x-h)^2 +y^2 = r^2 on the xy plane

Answer 3

since h > r, this means the x coordinate of the center is beyond the radius

Answer 4

so this means that the circle is guaranteed to be on the right side in this region

Answer 5

no...i'm in calc2 but i think some of these hideous problems may be calc3 stuff lol

Answer 6

because k = 0, we know the center of the circle must be on the x axis, so here is one circle that fits the equation and condition that (x-h)^2 +y^2 = r^2 , (h>r)

Answer 7

notice how the circle is in the region I highlighted, the center is on the x axis, and it's not touching the y axis

Answer 8

now if you spin the circle around the y axis, you would get something like this