Volume of a solid

[pauldw]

Find the volume of the solid formed by revolving the region bounded by the graphs of y=x^3, y=1 and x=2; About the line y=10. I am lost on these! Can someone please show me how to do it! Thanks
-Paul

 

[pauldw]

Hello

With that I get the result -166pi/7 which is not correct.
What am I doing wrong??
Also where did the 81 come from?

 

[galactus]

I'm sorry, try the absolute value. Is the answer 52*Pi.

The 81 comes from (1-10)^2.

 

[pauldw]

hello

no it is 265pi/7

 

[galactus]

Yes, I am afraid I made a booboo. Sorry.

Try using shells:

\(\displaystyle \L\\2{\pi}\int_{1}^{8}[(y-10)(y^{\frac{1}{3}}-2)]dy\)

I believe this one will give you the correct answer.

Try doing it with washers and see if you get the same.

 

[skeeter]

washers ...

\(\displaystyle \L V = \pi \int_1^2 9^2 - (10-x^3)^2 dx = \frac{265\pi}{7}\)