Homework SourseSketch the solid that lies above the cone z2 x2 y2 and is
Sketch the solid that lies above the cone z2 = x2 + y2 and is inside the sphere z2 + x2 + y2 = 4z. Write a description of the solid in terms of inequalities involving SPHERICAL coordinates. Write an interated triple integral in spherical coordinates needed to find the volume of the solid, and evaluate the volume.
Solution
standard equation of the sphere
x2+y2+(z-1/2)2=1/4
so center (0,0,1/2)
this tells us that equation equn. of the sphere is not in the form =c in spherical co-ordinates.
in spherical co-ordinates we have:
2=cos or =cos()
now the cone in spherical co ordinate will look like:
cos=sin or tan()=1 =>=/4
the solid will look like a ice-cream cone and in spherival co-ordinates
{(r,,)/(0<<cos,0<<2,0<</4)}
