Find the volume of the region enclosed by two spheres

Question

S₁ = x²+y²+z² = 1

S_{2 =} x²+y²+(z-2)² = 4

Answer 1

4pi/3(2^3-1^3)= 28pi but only if S1 is completely inside S2. It's not.

0 < volume < 28pi

center of S1 is the origin. S2 center is (0,0,2)

consider 2 dimensions

with circles comparable to the spheres:

x^2 +y^2 = 1

and x^2 + (y-2)^2 = 4

centers at the origin and (0,2)

radii = 1 and 2

draw a sketch, bottom or minimum point of the larger circle goes through the center of the smaller circle

similar situation with the two spheres

find where they intersect then that plane is like a chord in a circle

calculate the volumes of each from the chords to their respective surface

subtract that from 28pi