Thread: Finding Volume by Washer/Disk/Cylindrical Shell

1. 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?

2. 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.

3. 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- $x^2$

4. 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- $x^2$

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.

5. I see. Thank you very much for your help.

6. how to solve integral of similar plot

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?

7. 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 ?

8. horizontal strips since i need to do it using cylindrical shells