Regarding the question,

"Write down and evaluate triple integrals in spherical coordinates to determine the volume of the solid enclosed by the sphere x^2+y^2+z^2=4a^2 and the planes z=0 and z=a."

I am having trouble visualising the integration regions in normal and polar coordinates. Specifically, I am confused about why the bounds for r in the second integral range from 0 to 2a when the first integral goes from 0 to a*sec(phi).