Disk method.

**jeffjohnson** · March 3rd 2010, 02:36 PM

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

**skeeter** · March 3rd 2010, 02:43 PM

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 ...

$R = 2$

$r = \sqrt{y}$

$V = \pi \int_0^4 2^2 - (\sqrt{y})^2 \, dy<br />$

work it out ...

**Archie Meade** · March 3rd 2010, 02:51 PM

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,

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

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