# find exact volume of solid under...HELP!!!!!

• Mar 31st 2013, 05:27 AM
sluggerbroth
find exact volume of solid under...HELP!!!!!
hemisphere z=(4-x^(2)-y^(2))^(1/2) and above region bounded by the graph x^(2)+(y-1)^(2)=1
• Mar 31st 2013, 06:02 AM
HallsofIvy
Re: find exact volume of solid under...HELP!!!!!
Let $x= rcos(\theta)$ and $y= 1+ r sin(\theta)$. Then the hemisphere is given by $z= \sqrt{4- r^2cos^2(\theta)- (1+ rsin(\theta))^2}= \sqrt{5- r^2- 2rsin(\theta)}$ so the volume is
$\int_{r= 0}^1\int_{\theta= 0}^{2\pi}\sqrt{5- r^2- 2rsin(\theta)}d\theta dr$