The core (a cylinder with radius $r = 1$) is taken out of a sphere with radius $r = 4 $
Part 1: Write equations for the spherical surface + the cylindrical surface of the cylinder in rectangular coordinates, assuming they are centered on the origin.
Attempt. My answer so far: I assume these are just the standard equations for spherical surface: $$(x - a)^2 + (y - b)^2 + (z - c)^2 = r^2$$ and a right circular cylinder: $$x^2+y^2=a^2$$
Part 2: Draw each of the surfaces from part (a), separately; make sure to label reference points for scale (i.e. intercepts w/ axes).
Attempt. I know I can use traces to sketch this
Part 3: Find where the two surfaces intersect; express these intersection curves in terms of chosen coordinates.
Attempt. This part is puzzling me
Part 4: Find the volume outside of the cylinder and inside the sphere as a set of inequalities using the same coordinate system you used in part (c).
Attempt. This part is even more puzzling, not sure how to do this
Center your cylinder and sphere at the origin.
$x^2+y^2=1\\ x^2+y^2+z^2 = 4^2$
The intersection is a circle.
Subtract one equation from the other.
$z^2 = 15\\ z = \pm \sqrt {15}$
$x^2+y^2 = 1,$ and $z= \pm \sqrt {15}$
$V = \frac 43 \pi (\sqrt {15})^3$