Thread: Finding Volume by Washer/Disk/Cylindrical Shell

When finding the volume by either the washer, disk, or cylindrical shell, how would the limit be found?

Originally Posted by _rawr

When finding the volume by either the washer, disk, or cylindrical shell, how would the limit be found?

Give me an example of the question you are doing and l can show you.

Originally Posted by nyasha

Give me an example of the question you are doing and l can show you.

Find the volume of the solid that results when the shaded region is revolved around the x-axis.

y=x; y=2-

[When graphed, the shaded region is about the y=x line.]

Originally Posted by _rawr

Find the volume of the solid that results when the shaded region is revolved around the x-axis.

y=x; y=2-

[When graphed, the shaded region is about the y=x line.]

Find the intersections points of these two functions and those are your limits depending on whether you are using horizontal strips of vertical strips.


Note: The points of intersection are shown on the graph l uploaded. If using horizontal strips then take the y-values and if using the vertical strips then take the x-values.

I see. Thank you very much for your help.

i have this problem: find the volume of solid bounded by 2x+y=6 and y=4x^2 rotated about the x-axis using cylindrical shells... the book's answer is 250pi/3. but i can't seem to get that answer.

the plot is similar to that, and what i did is to separate the integrals into 2. one is the integral of 2*pi*y*(sqrt of y) from 0 to 4 and the second integral is the difference of the 2 functions. am i doing it right?

Originally Posted by ru_bled

i have this problem: find the volume of solid bounded by 2x+y=6 and y=4x^2 rotated about the x-axis using cylindrical shells... the book's answer is 250pi/3. but i can't seem to get that answer.

the plot is similar to that, and what i did is to separate the integrals into 2. one is the integral of 2*pi*y*(sqrt of y) from 0 to 4 and the second integral is the difference of the 2 functions. am i doing it right?

Are you using horizontal or vertical strips ?

horizontal strips since i need to do it using cylindrical shells