Homework Help: Volume generated

semc · Mar 22, 2010

Volume generated[Solved]

Use polar coordinates to find the volume of the given solid enclosed by the hyperboloid -x²-y²+z²=1 and the plane z=2.

I wrote out the integral [tex]\int\int 1+r^2 dr d\vartheta[/tex] integrated from 0 to [tex]2\pi[/tex] and r integrated from 0 to sqrt3 and volume enclosed gotten to be [tex]15\pi[/tex]/2. So this is the volume enclosed by the hyperboloid and the xy-plane correct? So I wanted to use the volume of the cyclinder to subtract off the volume found previously. But the volume is [tex]6\pi[/tex] so if I subtract i would get negative volume?

jav · Mar 22, 2010

Re: Volume generated[Solved]

semc said: ↑

Use polar coordinates to find the volume of the given solid enclosed by the hyperboloid -x²-y²+z²=1 and the plane z=2.

I wrote out the integral [tex]\int\int 1+r^2 dr d\vartheta[/tex] integrated from 0 to [tex]2\pi[/tex] and r integrated from 0 to sqrt3 and volume enclosed gotten to be [tex]15\pi[/tex]/2. So this is the volume enclosed by the hyperboloid and the xy-plane correct? So I wanted to use the volume of the cyclinder to subtract off the volume found previously. But the volume is [tex]6\pi[/tex] so if I subtract i would get negative volume?

It looks like you are integrating z^2 instead of z. Also shouldn't there be an extra r in the integral?

ie. [tex]\int\int z*r dr d\vartheta[/tex] whereas it looks like you are doing [tex]\int\int z^2 dr d\vartheta[/tex]

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Homework Help: Volume generated

semc

jav