I have a quick question to ask. How do you find the angle for the bottom angle ( as in the one that goes only up to 0 to pi(which is max).
I had a look at the solutions for this one apparently it goes from 0 to pi/4
find the volume of the smaller of the two regions bounded by the sphere x^2+y^2+z^2=16 and the cone z=sqrt(x^2+y^2).
thanks(im sorry if this looks familiar ..i def have not asked the above issue before)
In future, it would be helpful to tell us the situation you are looking at (here "find the volume of the smaller of the two regions bounded by the sphere x^2+y^2+z^2=16 and the cone z=sqrt(x^2+y^2)") first, then ask the question! Doing it the other way is confusing.
The "bottom angle" is the angle at the vertex of the cone, correct? In the xz-plane (y= 0) z= sqrt(x^2+ y^2) becomes z= sqrt(x^2)= |x| and so is a pair of lines z= x for x non-negative and z= -x for x negative. Each of those makes an angle of pi/4 with the x-axis and pi/2 with each other.