Volume of x^2+y^2=36, planes z=0 & x+y+12=z using spherical, cylindrical coord's

[chevyequinox2017]

I'm having trouble figuring out some problems that have to do with setting up triple integrals in cylindrical and spherical coordinates to find volumes of solids. The first problem states to use cylindrical coordinates to find the volume of the region closed by the cylinder x^2+y^2=36 and the planes z=0 and x+y+z=12. I know that x^2+y^2 is equal to r^2, so the radius would be 6, but I do not know the lower bound for r. I am also unsure of how to find the bounds for z and theta in this problem.

Another question states to use spherical coordinates to find the volume of the region enclosed by the cone z^2=x^2+y^2 between the planes z=4 and z=9. I think the bounds for rho would be zero to r^2 and the bounds for theta would be zero to 2 pi but I am unsure as to find the bounds for phi.

Can anyone help me on this?

 

[tkhunny]

Without obstruction, the lower bound for r is 0. Let's see your whole integral.