Mth101 Questio No1

• June 20th 2007, 01:48 AM
TAHIR
Mth101 Questio No1
Use cylindrical shells to find the volume of the solid generated when the region is enclosed by the given curves is revolved about the x-axis.
y^2=x, y=1, x=0
• June 20th 2007, 09:36 AM
curvature
Quote:

Originally Posted by TAHIR
Use cylindrical shells to find the volume of the solid generated when the region is enclosed by the given curves is revolved about the x-axis.
y^2=x, y=1, x=0

The region looks like this:
• June 20th 2007, 09:39 AM
curvature
Quote:

Originally Posted by TAHIR
Use cylindrical shells to find the volume of the solid generated when the region is enclosed by the given curves is revolved about the x-axis.
y^2=x, y=1, x=0

Why cylindrical shells? I think the washer method is better.
• June 20th 2007, 12:04 PM
earboth
Quote:

Originally Posted by TAHIR
Use cylindrical shells to find the volume of the solid generated when the region is enclosed by the given curves is revolved about the x-axis.
y^2=x, y=1, x=0

Hello,

I've used curvature's diagram to show you where you can find those cylindrical shells: see attachment.

One shell is calculated by:
$s=2 \pi y \cdot x$ Substitute $x = y^2$ into this equation and you'll get:
$s = 2 \pi y^3$

Now sum up all shells between the given bounds and you get the volume of the solid:

$V = \int_0^1 2 \pi y^3 dy = \left. \frac{1}{2} \pi y^4 \right|_0^1 = \frac{1}{2} \pi$