# Cylindrical shell (Check my answer)

• Apr 5th 2010, 08:24 AM
mj.alawami
Cylindrical shell (Check my answer)
Question :

Find the volume of the solid generated if the region bounded by the curve $\displaystyle y=x^2$ , $\displaystyle x=1$ is revolved about $\displaystyle x=0$.

Attempt:

I drew the figure and got ;

$\displaystyle V=2\pi r h t$

$\displaystyle 2\pi [\frac{x^3}{3}-\frac{x^4}{4}]\int$-limit from 1 to 0

= $\displaystyle \frac{\pi}{6}$
• Apr 5th 2010, 10:40 AM
eddie2042
Quote:

Originally Posted by mj.alawami
Question :

Find the volume of the solid generated if the region bounded by the curve $\displaystyle y=x^2$ , $\displaystyle x=1$ is revolved about $\displaystyle x=0$.

Attempt:

I drew the figure and got ;

$\displaystyle V=2\pi r h t$

$\displaystyle 2\pi [\frac{x^3}{3}-\frac{x^4}{4}]\int$-limit from 1 to 0

= $\displaystyle \frac{\pi}{6}$

You were mostly right. It should be

$\displaystyle V = \int_0^1 2\pi rh$
$\displaystyle V = 2\pi \int_0^1 x [x^2] dx$
$\displaystyle V = 2\pi \left[\frac{x^4}{4}\right]_0^1$
$\displaystyle V = \frac{\pi}{2}$