geometry.... help me please!

[ocgirl]

I was wondering if anyone could help me out on this problem.

I need to sketch the solid generated by rotating rectangle ABCD about the y axis and x-axis. Include the measurments.

A (4,1) B (7,1) C (7,8) and D (4,8)... these are the points for the rectangle. if anyone could explain how to do this it would be much appreciated.

Thanks!!!!!

OCGIRL~

 

[galactus]

Here's two methods for revolving about the x-axis. Use a similar approach for the y-axis.

SHELLS:

\(\displaystyle \L\\2{\pi}\int_{1}^{8}(3y)dy\)

WASHERS:

\(\displaystyle \L\\{\pi}\int_{4}^{7}(8^{2}-1^{2})dx\)


For shells, the cross-sections are parallel to the axis about which it is revolved.

If you use shells on your y-axis revolving, the cross-sections will be parallel to the y-axis, so, use x limits of integration.

For washers, use y limits of integration for revolving around y-axis.

 

[tkhunny]

I was wondering if anyone could help me out on this problem.

I need to sketch the solid generated by rotating rectangle ABCD about the y axis and x-axis. Include the measurments.

A (4,1) B (7,1) C (7,8) and D (4,8)... these are the points for the rectangle. if anyone could explain how to do this it would be much appreciated.

Geometry?

Can you say, "Right Circular Cyllinder"? Volume = pi*(r^2)*h

About the x-axis

You have an outer one: pi*((8)^2)*(7-4)
And core out a smaller one: pi*((1)^2)*(7-4)
Subtract.

You do the other one.

 

[soroban]

Hello, ocgirl!

I need to sketch the solid generated by rotating rectangle ABCD
about the y axis and x-axis. \(\displaystyle \;\)Include the measurments.

Vertices: \(\displaystyle \,A(4,1),\;B(7,1),\;C(7,8),\;D(4,8)\)

    |     (4,8)   (7,8)
   8+      D* - - - *C
    |       |       |
    |       |       |
    |       |       |
    |       |       |
    |       |       |
    |       |       |
   1+      A* - - - *B
    |     (4,1)   (7,1)
. --+-------+-------+--
    |       4       7

If we revolve the rectangle about the y-axis, the solid looks like this:

              *   *
          *           *
       *       * *       *
     *      *       *      *
    *     *           *     *
    *     *     +-----*-----*
    *     *       4   *  3  *
    |*      *       *      *|
    |  *       * *       *  |
    |     *           *     |
    |         *   *         |
    |                       | 7
    |                       |
    |                       |
    |                       |
    *                       *
    *                       *
     *                     *
       *                 *
          *           *
              *   *

That is what you asked for, isn't it? . . . a sketch?

 

[ocgirl]

more help!!! please

thats exactly what i needed but i have no clue how u solved that... more help please because i also need to figure out the x axis... unless u want to figure that one out too! i need it soon! asap!!!!


OCGIRL