# Disk method.

• Mar 3rd 2010, 02:36 PM
jeffjohnson
Disk method.
find the volume of the solid generated by revolving each region about the y-axis

the region in the first quadrant bounded above by the parabola y=x^2, below by the x, axis, and on the right by the line x=2.

Worked this problem out like 5 times idk why i cant get the right answer. cannot find what im doing wrong. It seems pretty simple. Answers 8Pi. HELP PLZ
• Mar 3rd 2010, 02:43 PM
skeeter
Quote:

Originally Posted by jeffjohnson
find the volume of the solid generated by revolving each region about the y-axis

the region in the first quadrant bounded above by the parabola y=x^2, below by the x, axis, and on the right by the line x=2.

Worked this problem out like 5 times idk why i cant get the right answer. cannot find what im doing wrong. It seems pretty simple. Answers 8Pi. HELP PLZ

washers ...

$\displaystyle R = 2$

$\displaystyle r = \sqrt{y}$

$\displaystyle V = \pi \int_0^4 2^2 - (\sqrt{y})^2 \, dy$

work it out ...
• Mar 3rd 2010, 02:51 PM
Quote:

Originally Posted by jeffjohnson
find the volume of the solid generated by revolving each region about the y-axis

the region in the first quadrant bounded above by the parabola y=x^2, below by the x, axis, and on the right by the line x=2.

Worked this problem out like 5 times idk why i cant get the right answer. cannot find what im doing wrong. It seems pretty simple. Answers 8Pi. HELP PLZ

Hi jeff,

using the integral of cylindrical surface areas,

$\displaystyle \int_{0}^22{\pi}\left((x)x^2\right)dx=2{\pi}\left( \frac{2^4}{4}\right)=\frac{2^5{\pi}}{4}$