# Triple integrals in cartesian and cylindrical coordinates

Can someone tell me why the answers highlighted in red ( 12 and pi/2 ) are wrong and how can I find the correct answers? The rest are correct

Thank you!

• Just draft the projection on the $xy$ plane and you'll immediately see what's wrong. Consider that $x^2+y^2=8y$ can be written as $x^2+(y-4)^2=16$.
– Yes
Mar 9 '17 at 2:45
• I'm sorry, I don't get it Mar 9 '17 at 2:58
• Since the projection on the $xy$ plane is a circle with a diameter of 8, it can be easily shown that $0\leq y\leq 8$.
– Yes
Mar 9 '17 at 3:09
• oh yeah you're right. what about the angle theta? Mar 9 '17 at 3:12
• To cover the whole domain you need $0\leq\theta\leq \pi$.
– Yes
Mar 9 '17 at 3:23