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

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- Jun 20th 2007, 12:48 AMTAHIRMth101 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 - Jun 20th 2007, 08:36 AMcurvature
- Jun 20th 2007, 08:39 AMcurvature
- Jun 20th 2007, 11:04 AMearboth
Hello,

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

One shell is calculated by:

$\displaystyle s=2 \pi y \cdot x$ Substitute $\displaystyle x = y^2$ into this equation and you'll get:

$\displaystyle s = 2 \pi y^3$

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

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