volume formed by rotating the region

**dat1611** · Aug 7th 2009, 07:28 AM

Find the volume formed by rotating the region enclosed by:
x=9y and y^3=x with y>=0
about the y-axis
can anyone help with this

**Failure** · Aug 7th 2009, 07:53 AM

Originally Posted by dat1611

Find the volume formed by rotating the region enclosed by:
x=9y and y^3=x with y>=0
about the y-axis
can anyone help with this

Well, the curves intersect at $(-3,-27), (0,0)$ and $(3,27)$ therefore:

By the method of rings you get

$V=\int\limits_0^3\pi \left[(9y)^2-(y^3)^2\right]\, dy$

By the method of cylinders you get

$V=\int\limits_0^{27}2\pi x(x^{1/3}-\tfrac{1}{9}x)\,dx$

Hopefully they are the same ( $V\approx 1308.69774$ ).

Thread: volume formed by rotating the region

LinkBack

Thread Tools

Display

volume formed by rotating the region

Similar Math Help Forum Discussions

Find the volume of the solid formed by rotating the region..

volume formed by rotating region

volume formed by rotating solid

volume of the solid region formed by intersection of two cylinders

volume of the solid formed by rotating the region

Search Tags