Use the washer method to find the volume of the solid generated by revolving the region bound by the lines and curves about the y-axis.

The semicircle x = sqrt(25 - y^2) and the line x = 4.

Thank you very much for your help!

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- Feb 15th 2010, 03:52 PMtorrentialVolumes of Revolution Question (Washer Method)
Use the washer method to find the volume of the solid generated by revolving the region bound by the lines and curves about the y-axis.

The semicircle x = sqrt(25 - y^2) and the line x = 4.

Thank you very much for your help! - Feb 15th 2010, 04:50 PMArchie Meade
hi torrential,

The washer radii are 4 and $\displaystyle \sqrt{25-y^2}$

When y=0, $\displaystyle x=\sqrt{25}=5$

Therefore the inner washer radii are 4.

The curve intersects the line when $\displaystyle 4=\sqrt{25-y^2}$

$\displaystyle 4=\sqrt{16},\ y^2=9,\ y=\pm3$

The surface area of inner disc is subtracted from the surface area of outer disc, to find the surface area of a washer.

We use x as the radius since x=0 is the axis of revolution.

Integrating these surfaces from y=-3 to 3 finds the vor.

The surface of a disc is $\displaystyle {\pi}r^2$ - Feb 15th 2010, 05:11 PMtorrential
(Clapping) Thank you very much! Your response really helped me!

- Feb 15th 2010, 05:34 PMArchie Meade
Cool!

So, you need to calculate

$\displaystyle \int_{-3}^3\left({\pi}(25-y^2)-(\pi)4^2\right)dy$