Volumes of Revolution Question (Washer Method)

• Feb 15th 2010, 04:52 PM
torrential
Volumes 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, 05:50 PM
Quote:

Originally Posted by torrential
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!

hi torrential,

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

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

Therefore the inner washer radii are 4.

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

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

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 ${\pi}r^2$
• Feb 15th 2010, 06:11 PM
torrential
(Clapping) Thank you very much! Your response really helped me!
• Feb 15th 2010, 06:34 PM
$\int_{-3}^3\left({\pi}(25-y^2)-(\pi)4^2\right)dy$